[{"language":[{"iso":"eng"}],"_id":"32573","user_id":"83504","department":[{"_id":"632"}],"status":"public","type":"conference","publication":"31st USENIX Security Symposium (USENIX Security 22)","title":"TLS-Anvil: Adapting Combinatorial Testing for TLS Libraries","publisher":"USENIX Association","date_updated":"2024-04-02T12:19:45Z","author":[{"last_name":"Maehren","full_name":"Maehren, Marcel","first_name":"Marcel"},{"last_name":"Nieting","full_name":"Nieting, Philipp","first_name":"Philipp"},{"last_name":"Hebrok","orcid":"0009-0006-1172-1665","full_name":"Hebrok, Sven Niclas","id":"55616","first_name":"Sven Niclas"},{"first_name":"Robert","full_name":"Merget, Robert","last_name":"Merget"},{"first_name":"Juraj","full_name":"Somorovsky, Juraj","id":"83504","last_name":"Somorovsky","orcid":"0000-0002-3593-7720"},{"first_name":"Jörg","last_name":"Schwenk","full_name":"Schwenk, Jörg"}],"date_created":"2022-08-03T11:03:30Z","year":"2022","place":"Boston, MA","citation":{"ama":"Maehren M, Nieting P, Hebrok SN, Merget R, Somorovsky J, Schwenk J. TLS-Anvil: Adapting Combinatorial Testing for TLS Libraries. In: 31st USENIX Security Symposium (USENIX Security 22). USENIX Association; 2022.","ieee":"M. Maehren, P. Nieting, S. N. Hebrok, R. Merget, J. Somorovsky, and J. Schwenk, “TLS-Anvil: Adapting Combinatorial Testing for TLS Libraries,” 2022.","chicago":"Maehren, Marcel, Philipp Nieting, Sven Niclas Hebrok, Robert Merget, Juraj Somorovsky, and Jörg Schwenk. “TLS-Anvil: Adapting Combinatorial Testing for TLS Libraries.” In 31st USENIX Security Symposium (USENIX Security 22). Boston, MA: USENIX Association, 2022.","bibtex":"@inproceedings{Maehren_Nieting_Hebrok_Merget_Somorovsky_Schwenk_2022, place={Boston, MA}, title={TLS-Anvil: Adapting Combinatorial Testing for TLS Libraries}, booktitle={31st USENIX Security Symposium (USENIX Security 22)}, publisher={USENIX Association}, author={Maehren, Marcel and Nieting, Philipp and Hebrok, Sven Niclas and Merget, Robert and Somorovsky, Juraj and Schwenk, Jörg}, year={2022} }","mla":"Maehren, Marcel, et al. “TLS-Anvil: Adapting Combinatorial Testing for TLS Libraries.” 31st USENIX Security Symposium (USENIX Security 22), USENIX Association, 2022.","short":"M. Maehren, P. Nieting, S.N. Hebrok, R. Merget, J. Somorovsky, J. Schwenk, in: 31st USENIX Security Symposium (USENIX Security 22), USENIX Association, Boston, MA, 2022.","apa":"Maehren, M., Nieting, P., Hebrok, S. N., Merget, R., Somorovsky, J., & Schwenk, J. (2022). TLS-Anvil: Adapting Combinatorial Testing for TLS Libraries. 31st USENIX Security Symposium (USENIX Security 22)."}},{"page":"259-278","citation":{"mla":"Büttner, Denise, and Tatienne Teichwart. “Reflektierendes Schreiben im Praxissemester. Eine Untersuchung studentischer Schreibprodukte im Kontext der Forschungswerkstätten „Sprachsensible Schulentwicklung“ im Masterstudiengang Bildungswissenschaften an der Universität Duisburg-Essen.” Fachorientierte Sprachbildung und sprachliche Vielfalt in der Lehrkräftebildung. Hochschuldidaktische Formate an der Universität Duisburg-Essen, edited by Katja F. Cantone et al., Waxmann, 2022, pp. 259–78.","short":"D. Büttner, T. Teichwart, in: K.F. Cantone, E. Gürsoy, I. Lammers, H. Roll (Eds.), Fachorientierte Sprachbildung und sprachliche Vielfalt in der Lehrkräftebildung. Hochschuldidaktische Formate an der Universität Duisburg-Essen, Waxmann, Münster, 2022, pp. 259–278.","bibtex":"@inbook{Büttner_Teichwart_2022, place={Münster}, title={Reflektierendes Schreiben im Praxissemester. Eine Untersuchung studentischer Schreibprodukte im Kontext der Forschungswerkstätten „Sprachsensible Schulentwicklung“ im Masterstudiengang Bildungswissenschaften an der Universität Duisburg-Essen}, booktitle={Fachorientierte Sprachbildung und sprachliche Vielfalt in der Lehrkräftebildung. Hochschuldidaktische Formate an der Universität Duisburg-Essen}, publisher={Waxmann}, author={Büttner, Denise and Teichwart, Tatienne}, editor={Cantone, Katja F. and Gürsoy, Erkan and Lammers, Ina and Roll, Heike}, year={2022}, pages={259–278} }","apa":"Büttner, D., & Teichwart, T. (2022). Reflektierendes Schreiben im Praxissemester. Eine Untersuchung studentischer Schreibprodukte im Kontext der Forschungswerkstätten „Sprachsensible Schulentwicklung“ im Masterstudiengang Bildungswissenschaften an der Universität Duisburg-Essen. In K. F. Cantone, E. Gürsoy, I. Lammers, & H. Roll (Eds.), Fachorientierte Sprachbildung und sprachliche Vielfalt in der Lehrkräftebildung. Hochschuldidaktische Formate an der Universität Duisburg-Essen (pp. 259–278). Waxmann.","ieee":"D. Büttner and T. Teichwart, “Reflektierendes Schreiben im Praxissemester. Eine Untersuchung studentischer Schreibprodukte im Kontext der Forschungswerkstätten „Sprachsensible Schulentwicklung“ im Masterstudiengang Bildungswissenschaften an der Universität Duisburg-Essen,” in Fachorientierte Sprachbildung und sprachliche Vielfalt in der Lehrkräftebildung. Hochschuldidaktische Formate an der Universität Duisburg-Essen, K. F. Cantone, E. Gürsoy, I. Lammers, and H. Roll, Eds. Münster: Waxmann, 2022, pp. 259–278.","chicago":"Büttner, Denise, and Tatienne Teichwart. “Reflektierendes Schreiben im Praxissemester. Eine Untersuchung studentischer Schreibprodukte im Kontext der Forschungswerkstätten „Sprachsensible Schulentwicklung“ im Masterstudiengang Bildungswissenschaften an der Universität Duisburg-Essen.” In Fachorientierte Sprachbildung und sprachliche Vielfalt in der Lehrkräftebildung. Hochschuldidaktische Formate an der Universität Duisburg-Essen, edited by Katja F. Cantone, Erkan Gürsoy, Ina Lammers, and Heike Roll, 259–78. Münster: Waxmann, 2022.","ama":"Büttner D, Teichwart T. Reflektierendes Schreiben im Praxissemester. Eine Untersuchung studentischer Schreibprodukte im Kontext der Forschungswerkstätten „Sprachsensible Schulentwicklung“ im Masterstudiengang Bildungswissenschaften an der Universität Duisburg-Essen. In: Cantone KF, Gürsoy E, Lammers I, Roll H, eds. Fachorientierte Sprachbildung und sprachliche Vielfalt in der Lehrkräftebildung. Hochschuldidaktische Formate an der Universität Duisburg-Essen. Waxmann; 2022:259-278."},"place":"Münster","year":"2022","title":"Reflektierendes Schreiben im Praxissemester. Eine Untersuchung studentischer Schreibprodukte im Kontext der Forschungswerkstätten „Sprachsensible Schulentwicklung“ im Masterstudiengang Bildungswissenschaften an der Universität Duisburg-Essen","author":[{"first_name":"Denise","full_name":"Büttner, Denise","id":"100819","last_name":"Büttner"},{"full_name":"Teichwart, Tatienne","last_name":"Teichwart","first_name":"Tatienne"}],"date_created":"2024-03-08T10:41:31Z","date_updated":"2024-04-02T13:03:58Z","publisher":"Waxmann","status":"public","editor":[{"first_name":"Katja F.","last_name":"Cantone","full_name":"Cantone, Katja F."},{"first_name":"Erkan","last_name":"Gürsoy","full_name":"Gürsoy, Erkan"},{"first_name":"Ina","full_name":"Lammers, Ina","last_name":"Lammers"},{"first_name":"Heike","last_name":"Roll","full_name":"Roll, Heike"}],"publication":"Fachorientierte Sprachbildung und sprachliche Vielfalt in der Lehrkräftebildung. Hochschuldidaktische Formate an der Universität Duisburg-Essen","type":"book_chapter","language":[{"iso":"ger"}],"department":[{"_id":"468"}],"user_id":"80828","_id":"52385"},{"title":"„Behinderung“ als Thema von Unterricht. Eine rekonstruktive Fallstudie zur (De-)Konstruktion von Dis*ability","main_file_link":[{"url":"https://link.springer.com/book/10.1007/978-3-658-37328-3","open_access":"1"}],"date_updated":"2024-04-02T13:04:32Z","oa":"1","publisher":"Springer","date_created":"2024-03-07T16:47:10Z","author":[{"first_name":"Denise","last_name":"Büttner","full_name":"Büttner, Denise","id":"100819"},{"last_name":"Frank","full_name":"Frank, Magnus","first_name":"Magnus"},{"first_name":"Thomas","full_name":"Geier, Thomas","last_name":"Geier"}],"place":"Wiesbaden","year":"2022","citation":{"ieee":"D. Büttner, M. Frank, and T. Geier, “„Behinderung“ als Thema von Unterricht. Eine rekonstruktive Fallstudie zur (De-)Konstruktion von Dis*ability,” in Lehren und Lernen in Differenzverhältnissen, Y. Akbaba, T. Buchner, A. M. B. Heinemann, D. Pokitsch, and T. Nadja, Eds. Wiesbaden: Springer, 2022, pp. 111–134.","chicago":"Büttner, Denise, Magnus Frank, and Thomas Geier. “„Behinderung“ als Thema von Unterricht. Eine rekonstruktive Fallstudie zur (De-)Konstruktion von Dis*ability.” In Lehren und Lernen in Differenzverhältnissen, edited by Yaliz Akbaba, Tobias Buchner, Alisha M.B. Heinemann, Doris Pokitsch, and Thomas Nadja, 111–34. Wiesbaden: Springer, 2022.","ama":"Büttner D, Frank M, Geier T. „Behinderung“ als Thema von Unterricht. Eine rekonstruktive Fallstudie zur (De-)Konstruktion von Dis*ability. In: Akbaba Y, Buchner T, Heinemann AMB, Pokitsch D, Nadja T, eds. Lehren und Lernen in Differenzverhältnissen. Springer; 2022:111-134.","apa":"Büttner, D., Frank, M., & Geier, T. (2022). „Behinderung“ als Thema von Unterricht. Eine rekonstruktive Fallstudie zur (De-)Konstruktion von Dis*ability. In Y. Akbaba, T. Buchner, A. M. B. Heinemann, D. Pokitsch, & T. Nadja (Eds.), Lehren und Lernen in Differenzverhältnissen (pp. 111–134). Springer.","bibtex":"@inbook{Büttner_Frank_Geier_2022, place={Wiesbaden}, title={„Behinderung“ als Thema von Unterricht. Eine rekonstruktive Fallstudie zur (De-)Konstruktion von Dis*ability}, booktitle={Lehren und Lernen in Differenzverhältnissen}, publisher={Springer}, author={Büttner, Denise and Frank, Magnus and Geier, Thomas}, editor={Akbaba, Yaliz and Buchner, Tobias and Heinemann, Alisha M.B. and Pokitsch, Doris and Nadja, Thomas}, year={2022}, pages={111–134} }","mla":"Büttner, Denise, et al. “„Behinderung“ als Thema von Unterricht. Eine rekonstruktive Fallstudie zur (De-)Konstruktion von Dis*ability.” Lehren und Lernen in Differenzverhältnissen, edited by Yaliz Akbaba et al., Springer, 2022, pp. 111–34.","short":"D. Büttner, M. Frank, T. Geier, in: Y. Akbaba, T. Buchner, A.M.B. Heinemann, D. Pokitsch, T. Nadja (Eds.), Lehren und Lernen in Differenzverhältnissen, Springer, Wiesbaden, 2022, pp. 111–134."},"page":"111-134","language":[{"iso":"ger"}],"_id":"52367","user_id":"80828","department":[{"_id":"468"}],"editor":[{"first_name":"Yaliz","full_name":"Akbaba, Yaliz","last_name":"Akbaba"},{"first_name":"Tobias","full_name":"Buchner, Tobias","last_name":"Buchner"},{"full_name":"Heinemann, Alisha M.B.","last_name":"Heinemann","first_name":"Alisha M.B."},{"first_name":"Doris","full_name":"Pokitsch, Doris","last_name":"Pokitsch"},{"last_name":"Nadja","full_name":"Nadja, Thomas","first_name":"Thomas"}],"status":"public","type":"book_chapter","publication":"Lehren und Lernen in Differenzverhältnissen"},{"year":"2022","citation":{"ama":"Frank M, Büttner D. “Bei dir läuft” - Zur Rekonstruktion neuer Sprache in Diskursen migrationsmarkierten Sprachwandels. MPZD. 2022;1(22):68-84.","chicago":"Frank, Magnus, and Denise Büttner. “‘Bei Dir Läuft’ - Zur Rekonstruktion Neuer Sprache in Diskursen Migrationsmarkierten Sprachwandels.” MPZD 1, no. 22 (2022): 68–84.","ieee":"M. Frank and D. Büttner, “‘Bei dir läuft’ - Zur Rekonstruktion neuer Sprache in Diskursen migrationsmarkierten Sprachwandels,” MPZD, vol. 1, no. 22, pp. 68–84, 2022.","apa":"Frank, M., & Büttner, D. (2022). “Bei dir läuft” - Zur Rekonstruktion neuer Sprache in Diskursen migrationsmarkierten Sprachwandels. MPZD, 1(22), 68–84.","short":"M. Frank, D. Büttner, MPZD 1 (2022) 68–84.","mla":"Frank, Magnus, and Denise Büttner. “‘Bei Dir Läuft’ - Zur Rekonstruktion Neuer Sprache in Diskursen Migrationsmarkierten Sprachwandels.” MPZD, vol. 1, no. 22, 2022, pp. 68–84.","bibtex":"@article{Frank_Büttner_2022, title={“Bei dir läuft” - Zur Rekonstruktion neuer Sprache in Diskursen migrationsmarkierten Sprachwandels}, volume={1}, number={22}, journal={MPZD}, author={Frank, Magnus and Büttner, Denise}, year={2022}, pages={68–84} }"},"page":"68-84","intvolume":" 1","issue":"22","title":"\"Bei dir läuft\" - Zur Rekonstruktion neuer Sprache in Diskursen migrationsmarkierten Sprachwandels","date_updated":"2024-04-02T13:04:09Z","author":[{"first_name":"Magnus","last_name":"Frank","full_name":"Frank, Magnus"},{"first_name":"Denise","last_name":"Büttner","id":"100819","full_name":"Büttner, Denise"}],"date_created":"2024-03-08T10:30:38Z","volume":1,"status":"public","type":"journal_article","publication":"MPZD","language":[{"iso":"eng"}],"_id":"52384","user_id":"80828","department":[{"_id":"468"}]},{"issue":"13","year":"2022","date_created":"2023-07-10T11:47:27Z","publisher":"World Scientific Pub Co Pte Ltd","title":"Viscoelastic Cahn–Hilliard models for tumor growth","publication":"Mathematical Models and Methods in Applied Sciences","abstract":[{"lang":"eng","text":" We introduce a new phase field model for tumor growth where viscoelastic effects are taken into account. The model is derived from basic thermodynamical principles and consists of a convected Cahn–Hilliard equation with source terms for the tumor cells and a convected reaction–diffusion equation with boundary supply for the nutrient. Chemotactic terms, which are essential for the invasive behavior of tumors, are taken into account. The model is completed by a viscoelastic system consisting of the Navier–Stokes equation for the hydrodynamic quantities, and a general constitutive equation with stress relaxation for the left Cauchy–Green tensor associated with the elastic part of the total mechanical response of the viscoelastic material. For a specific choice of the elastic energy density and with an additional dissipative term accounting for stress diffusion, we prove existence of global-in-time weak solutions of the viscoelastic model for tumor growth in two space dimensions [Formula: see text] by the passage to the limit in a fully-discrete finite element scheme where a CFL condition, i.e. [Formula: see text], is required. Moreover, in arbitrary dimensions [Formula: see text], we show stability and existence of solutions for the fully-discrete finite element scheme, where positive definiteness of the discrete Cauchy–Green tensor is proved with a regularization technique that was first introduced by Barrett and Boyaval [Existence and approximation of a (regularized) Oldroyd-B model, Math. Models Methods Appl. Sci. 21 (2011) 1783–1837]. After that, we improve the regularity results in arbitrary dimensions [Formula: see text] and in two dimensions [Formula: see text], where a CFL condition is required. Then, in two dimensions [Formula: see text], we pass to the limit in the discretization parameters and show that subsequences of discrete solutions converge to a global-in-time weak solution. Finally, we present numerical results in two dimensions [Formula: see text]. "}],"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Modeling and Simulation"],"publication_status":"published","publication_identifier":{"issn":["0218-2025","1793-6314"]},"citation":{"apa":"Garcke, H., Kovács, B., & Trautwein, D. (2022). Viscoelastic Cahn–Hilliard models for tumor growth. Mathematical Models and Methods in Applied Sciences, 32(13), 2673–2758. https://doi.org/10.1142/s0218202522500634","short":"H. Garcke, B. Kovács, D. Trautwein, Mathematical Models and Methods in Applied Sciences 32 (2022) 2673–2758.","bibtex":"@article{Garcke_Kovács_Trautwein_2022, title={Viscoelastic Cahn–Hilliard models for tumor growth}, volume={32}, DOI={10.1142/s0218202522500634}, number={13}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Garcke, Harald and Kovács, Balázs and Trautwein, Dennis}, year={2022}, pages={2673–2758} }","mla":"Garcke, Harald, et al. “Viscoelastic Cahn–Hilliard Models for Tumor Growth.” Mathematical Models and Methods in Applied Sciences, vol. 32, no. 13, World Scientific Pub Co Pte Ltd, 2022, pp. 2673–758, doi:10.1142/s0218202522500634.","ama":"Garcke H, Kovács B, Trautwein D. Viscoelastic Cahn–Hilliard models for tumor growth. Mathematical Models and Methods in Applied Sciences. 2022;32(13):2673-2758. doi:10.1142/s0218202522500634","ieee":"H. Garcke, B. Kovács, and D. Trautwein, “Viscoelastic Cahn–Hilliard models for tumor growth,” Mathematical Models and Methods in Applied Sciences, vol. 32, no. 13, pp. 2673–2758, 2022, doi: 10.1142/s0218202522500634.","chicago":"Garcke, Harald, Balázs Kovács, and Dennis Trautwein. “Viscoelastic Cahn–Hilliard Models for Tumor Growth.” Mathematical Models and Methods in Applied Sciences 32, no. 13 (2022): 2673–2758. https://doi.org/10.1142/s0218202522500634."},"page":"2673-2758","intvolume":" 32","author":[{"first_name":"Harald","last_name":"Garcke","full_name":"Garcke, Harald"},{"first_name":"Balázs","full_name":"Kovács, Balázs","id":"100441","orcid":"0000-0001-9872-3474","last_name":"Kovács"},{"full_name":"Trautwein, Dennis","last_name":"Trautwein","first_name":"Dennis"}],"volume":32,"date_updated":"2024-04-03T09:15:35Z","doi":"10.1142/s0218202522500634","type":"journal_article","status":"public","user_id":"100441","department":[{"_id":"841"}],"_id":"45970"},{"doi":"10.1007/s00211-022-01301-3","date_updated":"2024-04-03T09:15:44Z","author":[{"full_name":"Elliott, Charles M.","last_name":"Elliott","first_name":"Charles M."},{"first_name":"Harald","full_name":"Garcke, Harald","last_name":"Garcke"},{"first_name":"Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","full_name":"Kovács, Balázs","id":"100441"}],"volume":151,"citation":{"ama":"Elliott CM, Garcke H, Kovács B. Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. Numerische Mathematik. 2022;151(4):873-925. doi:10.1007/s00211-022-01301-3","chicago":"Elliott, Charles M., Harald Garcke, and Balázs Kovács. “Numerical Analysis for the Interaction of Mean Curvature Flow and Diffusion on Closed Surfaces.” Numerische Mathematik 151, no. 4 (2022): 873–925. https://doi.org/10.1007/s00211-022-01301-3.","ieee":"C. M. Elliott, H. Garcke, and B. Kovács, “Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces,” Numerische Mathematik, vol. 151, no. 4, pp. 873–925, 2022, doi: 10.1007/s00211-022-01301-3.","apa":"Elliott, C. M., Garcke, H., & Kovács, B. (2022). Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. Numerische Mathematik, 151(4), 873–925. https://doi.org/10.1007/s00211-022-01301-3","short":"C.M. Elliott, H. Garcke, B. Kovács, Numerische Mathematik 151 (2022) 873–925.","bibtex":"@article{Elliott_Garcke_Kovács_2022, title={Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces}, volume={151}, DOI={10.1007/s00211-022-01301-3}, number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Elliott, Charles M. and Garcke, Harald and Kovács, Balázs}, year={2022}, pages={873–925} }","mla":"Elliott, Charles M., et al. “Numerical Analysis for the Interaction of Mean Curvature Flow and Diffusion on Closed Surfaces.” Numerische Mathematik, vol. 151, no. 4, Springer Science and Business Media LLC, 2022, pp. 873–925, doi:10.1007/s00211-022-01301-3."},"page":"873-925","intvolume":" 151","publication_status":"published","publication_identifier":{"issn":["0029-599X","0945-3245"]},"_id":"45969","user_id":"100441","department":[{"_id":"841"}],"status":"public","type":"journal_article","title":"Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces","publisher":"Springer Science and Business Media LLC","date_created":"2023-07-10T11:47:11Z","year":"2022","issue":"4","keyword":["Applied Mathematics","Computational Mathematics"],"language":[{"iso":"eng"}],"abstract":[{"text":"AbstractAn evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction–diffusion process on the surface, inspired by a gradient flow of a coupled energy. Two algorithms are proposed, both based on a system coupling the diffusion equation to evolution equations for geometric quantities in the velocity law for the surface. One of the numerical methods is proved to be convergent in the$$H^1$$H1norm with optimal-order for finite elements of degree at least two. We present numerical experiments illustrating the convergence behaviour and demonstrating the qualitative properties of the flow: preservation of mean convexity, loss of convexity, weak maximum principles, and the occurrence of self-intersections.","lang":"eng"}],"publication":"Numerische Mathematik"},{"page":"1123-1164","intvolume":" 150","citation":{"ama":"Nick J, Kovács B, Lubich C. Time-dependent electromagnetic scattering from thin layers. Numerische Mathematik. 2022;150(4):1123-1164. doi:10.1007/s00211-022-01277-0","chicago":"Nick, Jörg, Balázs Kovács, and Christian Lubich. “Time-Dependent Electromagnetic Scattering from Thin Layers.” Numerische Mathematik 150, no. 4 (2022): 1123–64. https://doi.org/10.1007/s00211-022-01277-0.","ieee":"J. Nick, B. Kovács, and C. Lubich, “Time-dependent electromagnetic scattering from thin layers,” Numerische Mathematik, vol. 150, no. 4, pp. 1123–1164, 2022, doi: 10.1007/s00211-022-01277-0.","apa":"Nick, J., Kovács, B., & Lubich, C. (2022). Time-dependent electromagnetic scattering from thin layers. Numerische Mathematik, 150(4), 1123–1164. https://doi.org/10.1007/s00211-022-01277-0","short":"J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 150 (2022) 1123–1164.","mla":"Nick, Jörg, et al. “Time-Dependent Electromagnetic Scattering from Thin Layers.” Numerische Mathematik, vol. 150, no. 4, Springer Science and Business Media LLC, 2022, pp. 1123–64, doi:10.1007/s00211-022-01277-0.","bibtex":"@article{Nick_Kovács_Lubich_2022, title={Time-dependent electromagnetic scattering from thin layers}, volume={150}, DOI={10.1007/s00211-022-01277-0}, number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Nick, Jörg and Kovács, Balázs and Lubich, Christian}, year={2022}, pages={1123–1164} }"},"year":"2022","issue":"4","publication_identifier":{"issn":["0029-599X","0945-3245"]},"publication_status":"published","doi":"10.1007/s00211-022-01277-0","title":"Time-dependent electromagnetic scattering from thin layers","volume":150,"date_created":"2023-07-10T11:44:57Z","author":[{"full_name":"Nick, Jörg","last_name":"Nick","first_name":"Jörg"},{"orcid":"0000-0001-9872-3474","last_name":"Kovács","full_name":"Kovács, Balázs","id":"100441","first_name":"Balázs"},{"first_name":"Christian","full_name":"Lubich, Christian","last_name":"Lubich"}],"publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-03T09:18:23Z","status":"public","abstract":[{"text":"AbstractThe scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this includes a thin coating around a perfect conductor and the skin effect of a highly conducting material. The approach taken in this work is to derive, analyse and discretize a system of time-dependent boundary integral equations that determines the tangential traces of the scattered electric and magnetic fields. In a familiar second step, the fields are evaluated in the exterior domain by a representation formula, which uses the time-dependent potential operators of Maxwell’s equations. The time-dependent boundary integral equation is discretized with Runge–Kutta based convolution quadrature in time and Raviart–Thomas boundary elements in space. Using the frequency-explicit bounds from the well-posedness analysis given here together with known approximation properties of the numerical methods, the full discretization is proved to be stable and convergent, with explicitly given rates in the case of sufficient regularity. Taking the same Runge–Kutta based convolution quadrature for discretizing the time-dependent representation formulas, the optimal order of convergence is obtained away from the scattering boundary, whereas an order reduction occurs close to the boundary. The theoretical results are illustrated by numerical experiments.","lang":"eng"}],"publication":"Numerische Mathematik","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics"],"department":[{"_id":"841"}],"user_id":"100441","_id":"45963"},{"doi":"10.1093/imanum/drac033","title":"Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems","author":[{"first_name":"Balázs","id":"100441","full_name":"Kovács, Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474"},{"first_name":"Buyang","last_name":"Li","full_name":"Li, Buyang"}],"date_created":"2023-07-10T11:45:14Z","date_updated":"2024-04-03T09:17:59Z","publisher":"Oxford University Press (OUP)","citation":{"apa":"Kovács, B., & Li, B. (2022). Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems. IMA Journal of Numerical Analysis. https://doi.org/10.1093/imanum/drac033","short":"B. Kovács, B. Li, IMA Journal of Numerical Analysis (2022).","bibtex":"@article{Kovács_Li_2022, title={Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems}, DOI={10.1093/imanum/drac033}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Kovács, Balázs and Li, Buyang}, year={2022} }","mla":"Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.” IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2022, doi:10.1093/imanum/drac033.","ama":"Kovács B, Li B. Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems. IMA Journal of Numerical Analysis. Published online 2022. doi:10.1093/imanum/drac033","chicago":"Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.” IMA Journal of Numerical Analysis, 2022. https://doi.org/10.1093/imanum/drac033.","ieee":"B. Kovács and B. Li, “Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems,” IMA Journal of Numerical Analysis, 2022, doi: 10.1093/imanum/drac033."},"year":"2022","publication_status":"published","publication_identifier":{"issn":["0272-4979","1464-3642"]},"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"user_id":"100441","department":[{"_id":"841"}],"_id":"45964","status":"public","abstract":[{"text":"Abstract\r\n Maximal parabolic $L^p$-regularity of linear parabolic equations on an evolving surface is shown by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity on a fixed surface. By freezing the coefficients in the parabolic equations at a fixed time and utilizing a perturbation argument around the freezed time, it is shown that backward difference time discretizations of linear parabolic equations on an evolving surface along characteristic trajectories can preserve maximal $L^p$-regularity in the discrete setting. The result is applied to prove the stability and convergence of time discretizations of nonlinear parabolic equations on an evolving surface, with linearly implicit backward differentiation formulae characteristic trajectories of the surface, for general locally Lipschitz nonlinearities. The discrete maximal $L^p$-regularity is used to prove the boundedness and stability of numerical solutions in the $L^\\infty (0,T;W^{1,\\infty })$ norm, which is used to bound the nonlinear terms in the stability analysis. Optimal-order error estimates of time discretizations in the $L^\\infty (0,T;W^{1,\\infty })$ norm is obtained by combining the stability analysis with the consistency estimates.","lang":"eng"}],"type":"journal_article","publication":"IMA Journal of Numerical Analysis"},{"_id":"45966","department":[{"_id":"841"}],"user_id":"100441","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"publication":"IMA Journal of Numerical Analysis","type":"journal_article","abstract":[{"lang":"eng","text":"Abstract\r\n This paper studies bulk–surface splitting methods of first order for (semilinear) parabolic partial differential equations with dynamic boundary conditions. The proposed Lie splitting scheme is based on a reformulation of the problem as a coupled partial differential–algebraic equation system, i.e., the boundary conditions are considered as a second dynamic equation that is coupled to the bulk problem. The splitting approach is combined with bulk–surface finite elements and an implicit Euler discretization of the two subsystems. We prove first-order convergence of the resulting fully discrete scheme in the presence of a weak CFL condition of the form $\\tau \\leqslant c h$ for some constant $c>0$. The convergence is also illustrated numerically using dynamic boundary conditions of Allen–Cahn type."}],"status":"public","publisher":"Oxford University Press (OUP)","date_updated":"2024-04-03T09:16:47Z","volume":43,"author":[{"full_name":"Altmann, Robert","last_name":"Altmann","first_name":"Robert"},{"first_name":"Balázs","full_name":"Kovács, Balázs","id":"100441","last_name":"Kovács","orcid":"0000-0001-9872-3474"},{"first_name":"Christoph","last_name":"Zimmer","full_name":"Zimmer, Christoph"}],"date_created":"2023-07-10T11:45:49Z","title":"Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions","doi":"10.1093/imanum/drac002","publication_identifier":{"issn":["0272-4979","1464-3642"]},"publication_status":"published","issue":"2","year":"2022","intvolume":" 43","page":"950-975","citation":{"ama":"Altmann R, Kovács B, Zimmer C. Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions. IMA Journal of Numerical Analysis. 2022;43(2):950-975. doi:10.1093/imanum/drac002","chicago":"Altmann, Robert, Balázs Kovács, and Christoph Zimmer. “Bulk–Surface Lie Splitting for Parabolic Problems with Dynamic Boundary Conditions.” IMA Journal of Numerical Analysis 43, no. 2 (2022): 950–75. https://doi.org/10.1093/imanum/drac002.","ieee":"R. Altmann, B. Kovács, and C. Zimmer, “Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions,” IMA Journal of Numerical Analysis, vol. 43, no. 2, pp. 950–975, 2022, doi: 10.1093/imanum/drac002.","mla":"Altmann, Robert, et al. “Bulk–Surface Lie Splitting for Parabolic Problems with Dynamic Boundary Conditions.” IMA Journal of Numerical Analysis, vol. 43, no. 2, Oxford University Press (OUP), 2022, pp. 950–75, doi:10.1093/imanum/drac002.","short":"R. Altmann, B. Kovács, C. Zimmer, IMA Journal of Numerical Analysis 43 (2022) 950–975.","bibtex":"@article{Altmann_Kovács_Zimmer_2022, title={Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions}, volume={43}, DOI={10.1093/imanum/drac002}, number={2}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Altmann, Robert and Kovács, Balázs and Zimmer, Christoph}, year={2022}, pages={950–975} }","apa":"Altmann, R., Kovács, B., & Zimmer, C. (2022). Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions. IMA Journal of Numerical Analysis, 43(2), 950–975. https://doi.org/10.1093/imanum/drac002"}},{"publication":"IMA Journal of Numerical Analysis","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"Abstract\r\n We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components that describe the coupling and the dynamics in the abstract bulk- and surface-spaces, and treats the nonlinear terms similarly to an exponential integrator. The convergence proof is based on estimates for a recursive formulation of the error, using the parabolic smoothing property of analytic semigroups, and a careful comparison of the exact and approximate flows. This analysis also requires a deep understanding of the effects of the Dirichlet operator (the abstract version of the harmonic extension operator), which is essential for the stable coupling in our method. Numerical experiments, including problems with dynamic boundary conditions, reporting on convergence rates are presented."}],"department":[{"_id":"841"}],"user_id":"100441","_id":"45968","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"publication_identifier":{"issn":["0272-4979","1464-3642"]},"publication_status":"published","citation":{"apa":"Csomós, P., Farkas, B., & Kovács, B. (2022). Error estimates for a splitting integrator for abstract semilinear boundary coupled systems. IMA Journal of Numerical Analysis. https://doi.org/10.1093/imanum/drac079","mla":"Csomós, Petra, et al. “Error Estimates for a Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2022, doi:10.1093/imanum/drac079.","short":"P. Csomós, B. Farkas, B. Kovács, IMA Journal of Numerical Analysis (2022).","bibtex":"@article{Csomós_Farkas_Kovács_2022, title={Error estimates for a splitting integrator for abstract semilinear boundary coupled systems}, DOI={10.1093/imanum/drac079}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Csomós, Petra and Farkas, Bálint and Kovács, Balázs}, year={2022} }","ama":"Csomós P, Farkas B, Kovács B. Error estimates for a splitting integrator for abstract semilinear boundary coupled systems. IMA Journal of Numerical Analysis. Published online 2022. doi:10.1093/imanum/drac079","ieee":"P. Csomós, B. Farkas, and B. Kovács, “Error estimates for a splitting integrator for abstract semilinear boundary coupled systems,” IMA Journal of Numerical Analysis, 2022, doi: 10.1093/imanum/drac079.","chicago":"Csomós, Petra, Bálint Farkas, and Balázs Kovács. “Error Estimates for a Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” IMA Journal of Numerical Analysis, 2022. https://doi.org/10.1093/imanum/drac079."},"year":"2022","author":[{"first_name":"Petra","last_name":"Csomós","full_name":"Csomós, Petra"},{"first_name":"Bálint","full_name":"Farkas, Bálint","last_name":"Farkas"},{"last_name":"Kovács","orcid":"0000-0001-9872-3474","full_name":"Kovács, Balázs","id":"100441","first_name":"Balázs"}],"date_created":"2023-07-10T11:46:54Z","date_updated":"2024-04-03T09:15:52Z","publisher":"Oxford University Press (OUP)","doi":"10.1093/imanum/drac079","title":"Error estimates for a splitting integrator for abstract semilinear boundary coupled systems"},{"publication_status":"published","publication_identifier":{"issn":["0029-599X","0945-3245"]},"issue":"1","year":"2022","citation":{"short":"C.A. Beschle, B. Kovács, Numerische Mathematik 151 (2022) 1–48.","bibtex":"@article{Beschle_Kovács_2022, title={Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces}, volume={151}, DOI={10.1007/s00211-022-01280-5}, number={1}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Beschle, Cedric Aaron and Kovács, Balázs}, year={2022}, pages={1–48} }","mla":"Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates for Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” Numerische Mathematik, vol. 151, no. 1, Springer Science and Business Media LLC, 2022, pp. 1–48, doi:10.1007/s00211-022-01280-5.","apa":"Beschle, C. A., & Kovács, B. (2022). Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces. Numerische Mathematik, 151(1), 1–48. https://doi.org/10.1007/s00211-022-01280-5","ieee":"C. A. Beschle and B. Kovács, “Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces,” Numerische Mathematik, vol. 151, no. 1, pp. 1–48, 2022, doi: 10.1007/s00211-022-01280-5.","chicago":"Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates for Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” Numerische Mathematik 151, no. 1 (2022): 1–48. https://doi.org/10.1007/s00211-022-01280-5.","ama":"Beschle CA, Kovács B. Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces. Numerische Mathematik. 2022;151(1):1-48. doi:10.1007/s00211-022-01280-5"},"page":"1-48","intvolume":" 151","publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-03T09:19:34Z","date_created":"2023-07-10T11:43:44Z","author":[{"last_name":"Beschle","full_name":"Beschle, Cedric Aaron","first_name":"Cedric Aaron"},{"first_name":"Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","full_name":"Kovács, Balázs","id":"100441"}],"volume":151,"title":"Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces","doi":"10.1007/s00211-022-01280-5","type":"journal_article","publication":"Numerische Mathematik","abstract":[{"lang":"eng","text":"AbstractIn this paper, we consider a non-linear fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order evolving surface finite elements are used to discretise the weak equation system in space, and a modified matrix–vector formulation for the semi-discrete problem is derived. The anti-symmetric structure of the equation system is preserved by the spatial discretisation. A new stability proof, based on this structure, combined with consistency bounds proves optimal-order and uniform-in-time error estimates. The paper is concluded by a variety of numerical experiments."}],"status":"public","_id":"45958","user_id":"100441","department":[{"_id":"841"}],"keyword":["Applied Mathematics","Computational Mathematics"],"language":[{"iso":"eng"}]},{"abstract":[{"lang":"eng","text":"Abstract\r\n The full Maxwell equations in the unbounded three-dimensional space coupled to the Landau–Lifshitz–Gilbert equation serve as a well-tested model for ferromagnetic materials.\r\nWe propose a weak formulation of the coupled system based on the boundary integral formulation of the exterior Maxwell equations.\r\nWe show existence and partial uniqueness of a weak solution and propose a new numerical algorithm based on finite elements and boundary elements as spatial discretization with backward Euler and convolution quadrature for the time domain.\r\nThis is the first numerical algorithm which is able to deal with the coupled system of Landau–Lifshitz–Gilbert equation and full Maxwell’s equations without any simplifications like quasi-static approximations (e.g. eddy current model) and without restrictions on the shape of the domain (e.g. convexity).\r\nWe show well-posedness and convergence of the numerical algorithm under minimal assumptions on the regularity of the solution.\r\nThis is particularly important as there are few regularity results available and one generally expects the solution to be non-smooth.\r\nNumerical experiments illustrate and expand on the theoretical results."}],"publication":"Computational Methods in Applied Mathematics","keyword":["Applied Mathematics","Computational Mathematics","Numerical Analysis"],"language":[{"iso":"eng"}],"year":"2022","issue":"1","title":"FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation","publisher":"Walter de Gruyter GmbH","date_created":"2023-07-10T11:43:13Z","status":"public","type":"journal_article","_id":"45956","user_id":"100441","department":[{"_id":"841"}],"citation":{"short":"J. Bohn, M. Feischl, B. Kovács, Computational Methods in Applied Mathematics 23 (2022) 19–48.","bibtex":"@article{Bohn_Feischl_Kovács_2022, title={FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation}, volume={23}, DOI={10.1515/cmam-2022-0145}, number={1}, journal={Computational Methods in Applied Mathematics}, publisher={Walter de Gruyter GmbH}, author={Bohn, Jan and Feischl, Michael and Kovács, Balázs}, year={2022}, pages={19–48} }","mla":"Bohn, Jan, et al. “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation.” Computational Methods in Applied Mathematics, vol. 23, no. 1, Walter de Gruyter GmbH, 2022, pp. 19–48, doi:10.1515/cmam-2022-0145.","apa":"Bohn, J., Feischl, M., & Kovács, B. (2022). FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation. Computational Methods in Applied Mathematics, 23(1), 19–48. https://doi.org/10.1515/cmam-2022-0145","ieee":"J. Bohn, M. Feischl, and B. Kovács, “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation,” Computational Methods in Applied Mathematics, vol. 23, no. 1, pp. 19–48, 2022, doi: 10.1515/cmam-2022-0145.","chicago":"Bohn, Jan, Michael Feischl, and Balázs Kovács. “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation.” Computational Methods in Applied Mathematics 23, no. 1 (2022): 19–48. https://doi.org/10.1515/cmam-2022-0145.","ama":"Bohn J, Feischl M, Kovács B. FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation. Computational Methods in Applied Mathematics. 2022;23(1):19-48. doi:10.1515/cmam-2022-0145"},"page":"19-48","intvolume":" 23","publication_status":"published","publication_identifier":{"issn":["1609-4840","1609-9389"]},"doi":"10.1515/cmam-2022-0145","date_updated":"2024-04-03T09:20:30Z","author":[{"last_name":"Bohn","full_name":"Bohn, Jan","first_name":"Jan"},{"last_name":"Feischl","full_name":"Feischl, Michael","first_name":"Michael"},{"first_name":"Balázs","full_name":"Kovács, Balázs","id":"100441","last_name":"Kovács","orcid":"0000-0001-9872-3474"}],"volume":23},{"user_id":"105654","author":[{"first_name":"Ina","orcid":"0000-0003-0170-7713","last_name":"Krause","full_name":"Krause, Ina","id":"105654"}],"date_created":"2024-04-03T11:27:03Z","date_updated":"2024-04-03T11:27:18Z","_id":"53174","language":[{"iso":"eng"}],"title":"Distanzarbeit als Impulsgeber beruflicher Weiterbildung. Zur Bedeutung von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels von Büroarbeitswelten in und nach der Corona-Pandemie","type":"book_chapter","publication":"ZBW-Beiheft: Betriebliche Berufsbildungsforschung","citation":{"apa":"Krause, I. (2022). Distanzarbeit als Impulsgeber beruflicher Weiterbildung. Zur Bedeutung von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels von Büroarbeitswelten in und nach der Corona-Pandemie. In L. Bellmann, H. Ertl, C. Gerhards, & P. Sloane (Eds.), ZBW-Beiheft: Betriebliche Berufsbildungsforschung.","short":"I. Krause, in: L. Bellmann, H. Ertl, C. Gerhards, P. Sloane (Eds.), ZBW-Beiheft: Betriebliche Berufsbildungsforschung, 2022.","mla":"Krause, Ina. “Distanzarbeit Als Impulsgeber Beruflicher Weiterbildung. Zur Bedeutung von Neuen Schlüsselkompetenzen Und Weiterbildung Im Strukturwandels von Büroarbeitswelten in Und Nach Der Corona-Pandemie.” ZBW-Beiheft: Betriebliche Berufsbildungsforschung, edited by Lutz Bellmann et al., 2022.","bibtex":"@inbook{Krause_2022, title={Distanzarbeit als Impulsgeber beruflicher Weiterbildung. Zur Bedeutung von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels von Büroarbeitswelten in und nach der Corona-Pandemie}, booktitle={ZBW-Beiheft: Betriebliche Berufsbildungsforschung}, author={Krause, Ina}, editor={Bellmann, Lutz and Ertl, Hubert and Gerhards, Christian and Sloane, Peter}, year={2022} }","ieee":"I. Krause, “Distanzarbeit als Impulsgeber beruflicher Weiterbildung. Zur Bedeutung von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels von Büroarbeitswelten in und nach der Corona-Pandemie,” in ZBW-Beiheft: Betriebliche Berufsbildungsforschung, L. Bellmann, H. Ertl, C. Gerhards, and P. Sloane, Eds. 2022.","chicago":"Krause, Ina. “Distanzarbeit Als Impulsgeber Beruflicher Weiterbildung. Zur Bedeutung von Neuen Schlüsselkompetenzen Und Weiterbildung Im Strukturwandels von Büroarbeitswelten in Und Nach Der Corona-Pandemie.” In ZBW-Beiheft: Betriebliche Berufsbildungsforschung, edited by Lutz Bellmann, Hubert Ertl, Christian Gerhards, and Peter Sloane, 2022.","ama":"Krause I. Distanzarbeit als Impulsgeber beruflicher Weiterbildung. Zur Bedeutung von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels von Büroarbeitswelten in und nach der Corona-Pandemie. In: Bellmann L, Ertl H, Gerhards C, Sloane P, eds. ZBW-Beiheft: Betriebliche Berufsbildungsforschung. ; 2022."},"status":"public","year":"2022","editor":[{"first_name":"Lutz ","full_name":"Bellmann, Lutz ","last_name":"Bellmann"},{"full_name":"Ertl, Hubert","last_name":"Ertl","first_name":"Hubert"},{"last_name":"Gerhards","full_name":"Gerhards, Christian","first_name":"Christian"},{"full_name":"Sloane, Peter","last_name":"Sloane","first_name":"Peter"}]},{"user_id":"11871","department":[{"_id":"574"},{"_id":"760"}],"_id":"33740","language":[{"iso":"eng"}],"type":"book_chapter","publication":"The Semantic Web","status":"public","author":[{"first_name":"N'Dah Jean","last_name":"KOUAGOU","full_name":"KOUAGOU, N'Dah Jean","id":"87189"},{"first_name":"Stefan","id":"11871","full_name":"Heindorf, Stefan","last_name":"Heindorf","orcid":"0000-0002-4525-6865"},{"first_name":"Caglar","last_name":"Demir","id":"43817","full_name":"Demir, Caglar"},{"full_name":"Ngonga Ngomo, Axel-Cyrille","id":"65716","last_name":"Ngonga Ngomo","first_name":"Axel-Cyrille"}],"date_created":"2022-10-15T19:34:41Z","publisher":"Springer International Publishing","date_updated":"2024-04-03T13:26:10Z","oa":"1","main_file_link":[{"url":"https://arxiv.org/abs/2107.04911","open_access":"1"}],"doi":"10.1007/978-3-031-06981-9_14","title":"Learning Concept Lengths Accelerates Concept Learning in ALC","related_material":{"link":[{"relation":"confirmation","url":"https://link.springer.com/chapter/10.1007/978-3-031-06981-9_14"}]},"publication_status":"published","publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["9783031069802","9783031069819"]},"citation":{"ieee":"N. J. KOUAGOU, S. Heindorf, C. Demir, and A.-C. Ngonga Ngomo, “Learning Concept Lengths Accelerates Concept Learning in ALC,” in The Semantic Web, Cham: Springer International Publishing, 2022.","chicago":"KOUAGOU, N’Dah Jean, Stefan Heindorf, Caglar Demir, and Axel-Cyrille Ngonga Ngomo. “Learning Concept Lengths Accelerates Concept Learning in ALC.” In The Semantic Web. Cham: Springer International Publishing, 2022. https://doi.org/10.1007/978-3-031-06981-9_14.","ama":"KOUAGOU NJ, Heindorf S, Demir C, Ngonga Ngomo A-C. Learning Concept Lengths Accelerates Concept Learning in ALC. In: The Semantic Web. Springer International Publishing; 2022. doi:10.1007/978-3-031-06981-9_14","apa":"KOUAGOU, N. J., Heindorf, S., Demir, C., & Ngonga Ngomo, A.-C. (2022). Learning Concept Lengths Accelerates Concept Learning in ALC. In The Semantic Web. Springer International Publishing. https://doi.org/10.1007/978-3-031-06981-9_14","short":"N.J. KOUAGOU, S. Heindorf, C. Demir, A.-C. Ngonga Ngomo, in: The Semantic Web, Springer International Publishing, Cham, 2022.","bibtex":"@inbook{KOUAGOU_Heindorf_Demir_Ngonga Ngomo_2022, place={Cham}, title={Learning Concept Lengths Accelerates Concept Learning in ALC}, DOI={10.1007/978-3-031-06981-9_14}, booktitle={The Semantic Web}, publisher={Springer International Publishing}, author={KOUAGOU, N’Dah Jean and Heindorf, Stefan and Demir, Caglar and Ngonga Ngomo, Axel-Cyrille}, year={2022} }","mla":"KOUAGOU, N’Dah Jean, et al. “Learning Concept Lengths Accelerates Concept Learning in ALC.” The Semantic Web, Springer International Publishing, 2022, doi:10.1007/978-3-031-06981-9_14."},"place":"Cham","year":"2022"},{"date_created":"2024-04-05T09:04:01Z","author":[{"first_name":"Mohammad","last_name":"Soleymani","full_name":"Soleymani, Mohammad"},{"first_name":"Ignacio","last_name":"Santamaria","full_name":"Santamaria, Ignacio"},{"full_name":"Jorswieck, Eduard A.","last_name":"Jorswieck","first_name":"Eduard A."}],"volume":72,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","date_updated":"2024-04-05T13:21:31Z","doi":"10.1109/tvt.2022.3222633","title":"Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling","issue":"4","publication_status":"published","publication_identifier":{"issn":["0018-9545","1939-9359"]},"citation":{"short":"M. Soleymani, I. Santamaria, E.A. Jorswieck, IEEE Transactions on Vehicular Technology 72 (2022) 4580–4597.","mla":"Soleymani, Mohammad, et al. “Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling.” IEEE Transactions on Vehicular Technology, vol. 72, no. 4, Institute of Electrical and Electronics Engineers (IEEE), 2022, pp. 4580–97, doi:10.1109/tvt.2022.3222633.","bibtex":"@article{Soleymani_Santamaria_Jorswieck_2022, title={Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling}, volume={72}, DOI={10.1109/tvt.2022.3222633}, number={4}, journal={IEEE Transactions on Vehicular Technology}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Soleymani, Mohammad and Santamaria, Ignacio and Jorswieck, Eduard A.}, year={2022}, pages={4580–4597} }","apa":"Soleymani, M., Santamaria, I., & Jorswieck, E. A. (2022). Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling. IEEE Transactions on Vehicular Technology, 72(4), 4580–4597. https://doi.org/10.1109/tvt.2022.3222633","ama":"Soleymani M, Santamaria I, Jorswieck EA. Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling. IEEE Transactions on Vehicular Technology. 2022;72(4):4580-4597. doi:10.1109/tvt.2022.3222633","chicago":"Soleymani, Mohammad, Ignacio Santamaria, and Eduard A. Jorswieck. “Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling.” IEEE Transactions on Vehicular Technology 72, no. 4 (2022): 4580–97. https://doi.org/10.1109/tvt.2022.3222633.","ieee":"M. Soleymani, I. Santamaria, and E. A. Jorswieck, “Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling,” IEEE Transactions on Vehicular Technology, vol. 72, no. 4, pp. 4580–4597, 2022, doi: 10.1109/tvt.2022.3222633."},"page":"4580-4597","intvolume":" 72","year":"2022","user_id":"67076","department":[{"_id":"263"}],"_id":"53266","language":[{"iso":"eng"}],"keyword":["Electrical and Electronic Engineering","Computer Networks and Communications","Aerospace Engineering","Automotive Engineering"],"type":"journal_article","publication":"IEEE Transactions on Vehicular Technology","status":"public"},{"year":"2022","page":"723-738","intvolume":" 6","citation":{"ama":"Soleymani M, Santamaria I, Schreier PJ. Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance. IEEE Transactions on Green Communications and Networking. 2022;6(2):723-738. doi:10.1109/tgcn.2021.3140150","ieee":"M. Soleymani, I. Santamaria, and P. J. Schreier, “Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance,” IEEE Transactions on Green Communications and Networking, vol. 6, no. 2, pp. 723–738, 2022, doi: 10.1109/tgcn.2021.3140150.","chicago":"Soleymani, Mohammad, Ignacio Santamaria, and Peter J. Schreier. “Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance.” IEEE Transactions on Green Communications and Networking 6, no. 2 (2022): 723–38. https://doi.org/10.1109/tgcn.2021.3140150.","apa":"Soleymani, M., Santamaria, I., & Schreier, P. J. (2022). Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance. IEEE Transactions on Green Communications and Networking, 6(2), 723–738. https://doi.org/10.1109/tgcn.2021.3140150","bibtex":"@article{Soleymani_Santamaria_Schreier_2022, title={Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance}, volume={6}, DOI={10.1109/tgcn.2021.3140150}, number={2}, journal={IEEE Transactions on Green Communications and Networking}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Soleymani, Mohammad and Santamaria, Ignacio and Schreier, Peter J.}, year={2022}, pages={723–738} }","mla":"Soleymani, Mohammad, et al. “Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance.” IEEE Transactions on Green Communications and Networking, vol. 6, no. 2, Institute of Electrical and Electronics Engineers (IEEE), 2022, pp. 723–38, doi:10.1109/tgcn.2021.3140150.","short":"M. Soleymani, I. Santamaria, P.J. Schreier, IEEE Transactions on Green Communications and Networking 6 (2022) 723–738."},"publication_identifier":{"issn":["2473-2400"]},"publication_status":"published","issue":"2","title":"Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance","doi":"10.1109/tgcn.2021.3140150","date_updated":"2024-04-05T13:21:41Z","publisher":"Institute of Electrical and Electronics Engineers (IEEE)","volume":6,"date_created":"2024-04-05T09:04:25Z","author":[{"first_name":"Mohammad","full_name":"Soleymani, Mohammad","last_name":"Soleymani"},{"last_name":"Santamaria","full_name":"Santamaria, Ignacio","first_name":"Ignacio"},{"full_name":"Schreier, Peter J.","last_name":"Schreier","first_name":"Peter J."}],"status":"public","publication":"IEEE Transactions on Green Communications and Networking","type":"journal_article","keyword":["Computer Networks and Communications","Renewable Energy","Sustainability and the Environment"],"language":[{"iso":"eng"}],"_id":"53267","department":[{"_id":"263"}],"user_id":"67076"},{"user_id":"56070","_id":"53306","language":[{"iso":"eng"}],"publication":"Communications in Computer and Information Science","type":"book_chapter","status":"public","date_created":"2024-04-05T14:43:07Z","author":[{"first_name":"Hassan Ghasemzadeh","last_name":"Mohammadi","full_name":"Mohammadi, Hassan Ghasemzadeh"},{"last_name":"Jentzsch","full_name":"Jentzsch, Felix Paul","first_name":"Felix Paul"},{"last_name":"Kuschel","full_name":"Kuschel, Maurice","id":"56070","first_name":"Maurice"},{"first_name":"Rahil","last_name":"Arshad","full_name":"Arshad, Rahil"},{"last_name":"Rautmare","full_name":"Rautmare, Sneha","first_name":"Sneha"},{"first_name":"Suraj","full_name":"Manjunatha, Suraj","last_name":"Manjunatha"},{"first_name":"Marco","last_name":"Platzner","full_name":"Platzner, Marco"},{"last_name":"Boschmann","full_name":"Boschmann, Alexander","first_name":"Alexander"},{"full_name":"Schollbach, Dirk","last_name":"Schollbach","first_name":"Dirk"}],"date_updated":"2024-04-05T14:50:26Z","publisher":"Springer International Publishing","doi":"10.1007/978-3-030-93736-2_27","title":"FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics","publication_identifier":{"isbn":["9783030937355","9783030937362"],"issn":["1865-0929","1865-0937"]},"publication_status":"published","citation":{"ama":"Mohammadi HG, Jentzsch FP, Kuschel M, et al. FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics. In: Communications in Computer and Information Science. Springer International Publishing; 2022. doi:10.1007/978-3-030-93736-2_27","ieee":"H. G. Mohammadi et al., “FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics,” in Communications in Computer and Information Science, Cham: Springer International Publishing, 2022.","chicago":"Mohammadi, Hassan Ghasemzadeh, Felix Paul Jentzsch, Maurice Kuschel, Rahil Arshad, Sneha Rautmare, Suraj Manjunatha, Marco Platzner, Alexander Boschmann, and Dirk Schollbach. “FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics.” In Communications in Computer and Information Science. Cham: Springer International Publishing, 2022. https://doi.org/10.1007/978-3-030-93736-2_27.","bibtex":"@inbook{Mohammadi_Jentzsch_Kuschel_Arshad_Rautmare_Manjunatha_Platzner_Boschmann_Schollbach_2022, place={Cham}, title={FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics}, DOI={10.1007/978-3-030-93736-2_27}, booktitle={Communications in Computer and Information Science}, publisher={Springer International Publishing}, author={Mohammadi, Hassan Ghasemzadeh and Jentzsch, Felix Paul and Kuschel, Maurice and Arshad, Rahil and Rautmare, Sneha and Manjunatha, Suraj and Platzner, Marco and Boschmann, Alexander and Schollbach, Dirk}, year={2022} }","mla":"Mohammadi, Hassan Ghasemzadeh, et al. “FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics.” Communications in Computer and Information Science, Springer International Publishing, 2022, doi:10.1007/978-3-030-93736-2_27.","short":"H.G. Mohammadi, F.P. Jentzsch, M. Kuschel, R. Arshad, S. Rautmare, S. Manjunatha, M. Platzner, A. Boschmann, D. Schollbach, in: Communications in Computer and Information Science, Springer International Publishing, Cham, 2022.","apa":"Mohammadi, H. G., Jentzsch, F. P., Kuschel, M., Arshad, R., Rautmare, S., Manjunatha, S., Platzner, M., Boschmann, A., & Schollbach, D. (2022). FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics. In Communications in Computer and Information Science. Springer International Publishing. https://doi.org/10.1007/978-3-030-93736-2_27"},"place":"Cham","year":"2022"},{"type":"journal_article","publication":"International Mathematics Research Notices","abstract":[{"lang":"eng","text":"Abstract\r\n The Neumann problem for (0.1)$$ \\begin{align}& V_t = \\Delta V-aV+f(x,t) \\end{align}$$is considered in bounded domains $\\Omega \\subset {\\mathbb {R}}^n$ with smooth boundary, where $n\\ge 1$ and $a\\in {\\mathbb {R}}$. By means of a variational approach, a statement on boundedness of the quantities $$ \\begin{eqnarray*} \\sup_{t\\in (0,T)} \\int_\\Omega \\big|\\nabla V(\\cdot,t)\\big|^p L^{\\frac{n+p}{n+2}} \\Big( \\big|\\nabla V(\\cdot,t)\\big| \\Big) \\end{eqnarray*}$$in dependence on the expressions (0.2)$$ \\begin{align}& \\sup_{t\\in (0,T-\\tau)} \\int_t^{t+\\tau} \\int_\\Omega |f|^{\\frac{(n+2)p}{n+p}} L\\big( |f|\\big) \\end{align}$$is derived for $p\\ge 2$, $\\tau>0$, and $T\\ge 2\\tau $, provided that $L\\in C^0([0,\\infty ))$ is positive, strictly increasing, unbounded, and slowly growing in the sense that $\\limsup _{s\\to \\infty } \\frac {L(s^{\\lambda _0})}{L(s)} <\\infty $ for some $\\lambda _0>1$. In the particular case when $p=n\\ge 2$, an additional condition on growth of $L$, particularly satisfied by $L(\\xi ):=\\ln ^\\alpha (\\xi +b)$ whenever $b>0$ and $\\alpha>\\frac {(n+2)(n-1)}{2n}$, is identified as sufficient to ensure that as a consequence of the above, bounds for theintegrals in (0.2) even imply estimates for the spatio-temporal modulus of continuity of solutions to (0.1). A subsequent application to the Keller–Segel system $$ \\begin{eqnarray*} \\left\\{ \\begin{array}{l} u_t = \\nabla \\cdot \\big( D(v)\\nabla u\\big) - \\nabla \\cdot \\big( uS(v)\\nabla v\\big) + ru - \\mu u^2, \\\\[1mm] v_t = \\Delta v-v+u, \\end{array} \\right. \\end{eqnarray*}$$shows that when $n=2$, $r\\in {\\mathbb {R}}$, $0<D\\in C^2([0,\\infty ))$, and $S\\in C^2([0,\\infty )) \\cap W^{1,\\infty }((0,\\infty ))$ and thus especially in the presence of arbitrarily strong diffusion degeneracies implied by rapid decay of $D$, any choice of $\\mu>0$ excludes blowup in the sense that for all suitably regular nonnegative initial data, an associated initial-boundary value problem admits a global bounded classical solution."}],"status":"public","_id":"53319","user_id":"31496","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1073-7928","1687-0247"]},"issue":"19","year":"2022","citation":{"mla":"Winkler, Michael. “A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System.” International Mathematics Research Notices, vol. 2023, no. 19, Oxford University Press (OUP), 2022, pp. 16336–93, doi:10.1093/imrn/rnac286.","bibtex":"@article{Winkler_2022, title={A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System}, volume={2023}, DOI={10.1093/imrn/rnac286}, number={19}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Winkler, Michael}, year={2022}, pages={16336–16393} }","short":"M. Winkler, International Mathematics Research Notices 2023 (2022) 16336–16393.","apa":"Winkler, M. (2022). A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System. International Mathematics Research Notices, 2023(19), 16336–16393. https://doi.org/10.1093/imrn/rnac286","chicago":"Winkler, Michael. “A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System.” International Mathematics Research Notices 2023, no. 19 (2022): 16336–93. https://doi.org/10.1093/imrn/rnac286.","ieee":"M. Winkler, “A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System,” International Mathematics Research Notices, vol. 2023, no. 19, pp. 16336–16393, 2022, doi: 10.1093/imrn/rnac286.","ama":"Winkler M. A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System. International Mathematics Research Notices. 2022;2023(19):16336-16393. doi:10.1093/imrn/rnac286"},"page":"16336-16393","intvolume":" 2023","date_updated":"2024-04-07T12:36:06Z","publisher":"Oxford University Press (OUP)","author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"date_created":"2024-04-07T12:33:44Z","volume":2023,"title":"A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System","doi":"10.1093/imrn/rnac286"},{"publication_identifier":{"issn":["0219-1997","1793-6683"]},"publication_status":"published","issue":"10","year":"2022","intvolume":" 25","citation":{"mla":"Winkler, Michael. “Arbitrarily Fast Grow-up Rates in Quasilinear Keller–Segel Systems.” Communications in Contemporary Mathematics, vol. 25, no. 10, World Scientific Pub Co Pte Ltd, 2022, doi:10.1142/s0219199722500626.","short":"M. Winkler, Communications in Contemporary Mathematics 25 (2022).","bibtex":"@article{Winkler_2022, title={Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems}, volume={25}, DOI={10.1142/s0219199722500626}, number={10}, journal={Communications in Contemporary Mathematics}, publisher={World Scientific Pub Co Pte Ltd}, author={Winkler, Michael}, year={2022} }","apa":"Winkler, M. (2022). Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems. Communications in Contemporary Mathematics, 25(10). https://doi.org/10.1142/s0219199722500626","ieee":"M. Winkler, “Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems,” Communications in Contemporary Mathematics, vol. 25, no. 10, 2022, doi: 10.1142/s0219199722500626.","chicago":"Winkler, Michael. “Arbitrarily Fast Grow-up Rates in Quasilinear Keller–Segel Systems.” Communications in Contemporary Mathematics 25, no. 10 (2022). https://doi.org/10.1142/s0219199722500626.","ama":"Winkler M. Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems. Communications in Contemporary Mathematics. 2022;25(10). doi:10.1142/s0219199722500626"},"publisher":"World Scientific Pub Co Pte Ltd","date_updated":"2024-04-07T12:35:53Z","volume":25,"date_created":"2024-04-07T12:35:09Z","author":[{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"title":"Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems","doi":"10.1142/s0219199722500626","publication":"Communications in Contemporary Mathematics","type":"journal_article","abstract":[{"lang":"eng","text":" The chemotaxis system [Formula: see text] is considered in a ball [Formula: see text], [Formula: see text], where the positive function [Formula: see text] reflects suitably weak diffusion by satisfying [Formula: see text] for some [Formula: see text]. It is shown that whenever [Formula: see text] is positive and satisfies [Formula: see text] as [Formula: see text], one can find a suitably regular nonlinearity [Formula: see text] with the property that at each sufficiently large mass level [Formula: see text] there exists a globally defined radially symmetric classical solution to a Neumann-type boundary value problem for (⋆) which satisfies [Formula: see text] "}],"status":"public","_id":"53321","user_id":"31496","keyword":["Applied Mathematics","General Mathematics"],"language":[{"iso":"eng"}]},{"publication_status":"published","publication_identifier":{"issn":["1040-7294","1572-9222"]},"year":"2022","citation":{"bibtex":"@article{Winkler_2022, title={Slow Grow-up in a Quasilinear Keller–Segel System}, DOI={10.1007/s10884-022-10167-w}, journal={Journal of Dynamics and Differential Equations}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2022} }","short":"M. Winkler, Journal of Dynamics and Differential Equations (2022).","mla":"Winkler, Michael. “Slow Grow-up in a Quasilinear Keller–Segel System.” Journal of Dynamics and Differential Equations, Springer Science and Business Media LLC, 2022, doi:10.1007/s10884-022-10167-w.","apa":"Winkler, M. (2022). Slow Grow-up in a Quasilinear Keller–Segel System. Journal of Dynamics and Differential Equations. https://doi.org/10.1007/s10884-022-10167-w","ama":"Winkler M. Slow Grow-up in a Quasilinear Keller–Segel System. Journal of Dynamics and Differential Equations. Published online 2022. doi:10.1007/s10884-022-10167-w","chicago":"Winkler, Michael. “Slow Grow-up in a Quasilinear Keller–Segel System.” Journal of Dynamics and Differential Equations, 2022. https://doi.org/10.1007/s10884-022-10167-w.","ieee":"M. Winkler, “Slow Grow-up in a Quasilinear Keller–Segel System,” Journal of Dynamics and Differential Equations, 2022, doi: 10.1007/s10884-022-10167-w."},"publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-07T12:39:17Z","date_created":"2024-04-07T12:39:12Z","author":[{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"title":"Slow Grow-up in a Quasilinear Keller–Segel System","doi":"10.1007/s10884-022-10167-w","type":"journal_article","publication":"Journal of Dynamics and Differential Equations","abstract":[{"text":"AbstractIn a ball $$\\Omega =B_R(0)\\subset \\mathbb {R}^n$$\r\n \r\n Ω\r\n =\r\n \r\n B\r\n R\r\n \r\n \r\n (\r\n 0\r\n )\r\n \r\n ⊂\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n \r\n , $$n\\ge 2$$\r\n \r\n n\r\n ≥\r\n 2\r\n \r\n , the chemotaxis system $$\\begin{aligned} \\left\\{ \\begin{array}{l}u_t = \\nabla \\cdot \\big ( D(u) \\nabla u \\big ) - \\nabla \\cdot \\big ( uS(u)\\nabla v\\big ), \\\\ 0 = \\Delta v - \\mu + u, \\qquad \\mu =\\frac{1}{|\\Omega |} \\int _\\Omega u, \\end{array} \\right. \\qquad \\qquad (\\star ) \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n =\r\n ∇\r\n ·\r\n \r\n (\r\n \r\n D\r\n \r\n (\r\n u\r\n )\r\n \r\n ∇\r\n u\r\n \r\n )\r\n \r\n -\r\n ∇\r\n ·\r\n \r\n (\r\n \r\n u\r\n S\r\n \r\n (\r\n u\r\n )\r\n \r\n ∇\r\n v\r\n \r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n 0\r\n =\r\n Δ\r\n v\r\n -\r\n μ\r\n +\r\n u\r\n ,\r\n \r\n μ\r\n =\r\n \r\n 1\r\n \r\n |\r\n Ω\r\n |\r\n \r\n \r\n \r\n ∫\r\n Ω\r\n \r\n u\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n (\r\n ⋆\r\n )\r\n \r\n \r\n \r\n \r\n \r\n \r\n is considered under no-flux boundary conditions, with a focus on nonlinearities $$S\\in C^2([0,\\infty ))$$\r\n \r\n S\r\n ∈\r\n \r\n C\r\n 2\r\n \r\n \r\n (\r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n which exhibit super-algebraically fast decay in the sense that with some $$K_S>0, \\beta \\in [0,1)$$\r\n \r\n \r\n K\r\n S\r\n \r\n >\r\n 0\r\n ,\r\n β\r\n ∈\r\n \r\n [\r\n 0\r\n ,\r\n 1\r\n )\r\n \r\n \r\n and $$\\xi _0>0$$\r\n \r\n \r\n ξ\r\n 0\r\n \r\n >\r\n 0\r\n \r\n , $$\\begin{aligned} S(\\xi )>0 \\quad \\text{ and } \\quad S'(\\xi ) \\le -K_S\\xi ^{-\\beta } S(\\xi ) \\qquad \\text{ for } \\text{ all } \\xi \\ge \\xi _0. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n S\r\n \r\n (\r\n ξ\r\n )\r\n \r\n >\r\n 0\r\n \r\n \r\n and\r\n \r\n \r\n \r\n S\r\n ′\r\n \r\n \r\n (\r\n ξ\r\n )\r\n \r\n ≤\r\n -\r\n \r\n K\r\n S\r\n \r\n \r\n ξ\r\n \r\n -\r\n β\r\n \r\n \r\n S\r\n \r\n (\r\n ξ\r\n )\r\n \r\n \r\n \r\n for\r\n \r\n \r\n all\r\n \r\n ξ\r\n ≥\r\n \r\n ξ\r\n 0\r\n \r\n .\r\n \r\n \r\n \r\n \r\n \r\n It is, inter alia, shown that if furthermore $$D\\in C^2((0,\\infty ))$$\r\n \r\n D\r\n ∈\r\n \r\n C\r\n 2\r\n \r\n \r\n (\r\n \r\n (\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n is positive and suitably small in relation to S by satisfying $$\\begin{aligned} \\frac{\\xi S(\\xi )}{D(\\xi )} \\ge K_{SD}\\xi ^\\lambda \\qquad \\text{ for } \\text{ all } \\xi \\ge \\xi _0 \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n ξ\r\n S\r\n (\r\n ξ\r\n )\r\n \r\n \r\n D\r\n (\r\n ξ\r\n )\r\n \r\n \r\n ≥\r\n \r\n K\r\n \r\n SD\r\n \r\n \r\n \r\n ξ\r\n λ\r\n \r\n \r\n \r\n for\r\n \r\n \r\n all\r\n \r\n ξ\r\n ≥\r\n \r\n ξ\r\n 0\r\n \r\n \r\n \r\n \r\n \r\n \r\n with some $$K_{SD}>0$$\r\n \r\n \r\n K\r\n \r\n SD\r\n \r\n \r\n >\r\n 0\r\n \r\n and $$\\lambda >\\frac{2}{n}$$\r\n \r\n λ\r\n >\r\n \r\n 2\r\n n\r\n \r\n \r\n , then throughout a considerably large set of initial data, ($$\\star $$\r\n ⋆\r\n ) admits global classical solutions (u, v) fulfilling $$\\begin{aligned} \\frac{z(t)}{C} \\le \\Vert u(\\cdot ,t)\\Vert _{L^\\infty (\\Omega )} \\le Cz(t) \\qquad \\text{ for } \\text{ all } t>0, \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n z\r\n (\r\n t\r\n )\r\n \r\n C\r\n \r\n ≤\r\n \r\n \r\n ‖\r\n u\r\n \r\n (\r\n ·\r\n ,\r\n t\r\n )\r\n \r\n ‖\r\n \r\n \r\n \r\n L\r\n ∞\r\n \r\n \r\n (\r\n Ω\r\n )\r\n \r\n \r\n \r\n ≤\r\n C\r\n z\r\n \r\n (\r\n t\r\n )\r\n \r\n \r\n \r\n for\r\n \r\n \r\n all\r\n \r\n t\r\n >\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n with some $$C=C^{(u,v)}\\ge 1$$\r\n \r\n C\r\n =\r\n \r\n C\r\n \r\n (\r\n u\r\n ,\r\n v\r\n )\r\n \r\n \r\n ≥\r\n 1\r\n \r\n , where z denotes the solution of $$\\begin{aligned} \\left\\{ \\begin{array}{l}z'(t) = z^2(t) \\cdot S\\big ( z(t)\\big ), \\qquad t>0, \\\\ z(0)=\\xi _0, \\end{array} \\right. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n z\r\n ′\r\n \r\n \r\n (\r\n t\r\n )\r\n \r\n =\r\n \r\n z\r\n 2\r\n \r\n \r\n (\r\n t\r\n )\r\n \r\n ·\r\n S\r\n \r\n (\r\n \r\n z\r\n \r\n (\r\n t\r\n )\r\n \r\n \r\n )\r\n \r\n ,\r\n \r\n t\r\n >\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n z\r\n \r\n (\r\n 0\r\n )\r\n \r\n =\r\n \r\n ξ\r\n 0\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n which is seen to exist globally, and to satisfy $$z(t)\\rightarrow +\\infty $$\r\n \r\n z\r\n (\r\n t\r\n )\r\n →\r\n +\r\n ∞\r\n \r\n as $$t\\rightarrow \\infty $$\r\n \r\n t\r\n →\r\n ∞\r\n \r\n . As particular examples, exponentially and doubly exponentially decaying S are found to imply corresponding infinite-time blow-up properties in ($$\\star $$\r\n ⋆\r\n ) at logarithmic and doubly logarithmic rates, respectively.","lang":"eng"}],"status":"public","_id":"53323","user_id":"31496","keyword":["Analysis"],"language":[{"iso":"eng"}]}]