--- _id: '47562' article_number: '117632' author: - first_name: Felix full_name: Herrmann, Felix last_name: Herrmann - first_name: Marcus full_name: Grünewald, Marcus last_name: Grünewald - first_name: Tobias full_name: Meijer, Tobias last_name: Meijer - first_name: Ulrich full_name: Gardemann, Ulrich last_name: Gardemann - first_name: Lukas full_name: Feierabend, Lukas last_name: Feierabend - first_name: Julia full_name: Riese, Julia id: '101499' last_name: Riese orcid: 0000-0002-3053-0534 citation: ama: Herrmann F, Grünewald M, Meijer T, Gardemann U, Feierabend L, Riese J. Operating window and flexibility of a lab-scale methanation plant. Chemical Engineering Science. 2022;254. doi:10.1016/j.ces.2022.117632 apa: Herrmann, F., Grünewald, M., Meijer, T., Gardemann, U., Feierabend, L., & Riese, J. (2022). Operating window and flexibility of a lab-scale methanation plant. Chemical Engineering Science, 254, Article 117632. https://doi.org/10.1016/j.ces.2022.117632 bibtex: '@article{Herrmann_Grünewald_Meijer_Gardemann_Feierabend_Riese_2022, title={Operating window and flexibility of a lab-scale methanation plant}, volume={254}, DOI={10.1016/j.ces.2022.117632}, number={117632}, journal={Chemical Engineering Science}, publisher={Elsevier BV}, author={Herrmann, Felix and Grünewald, Marcus and Meijer, Tobias and Gardemann, Ulrich and Feierabend, Lukas and Riese, Julia}, year={2022} }' chicago: Herrmann, Felix, Marcus Grünewald, Tobias Meijer, Ulrich Gardemann, Lukas Feierabend, and Julia Riese. “Operating Window and Flexibility of a Lab-Scale Methanation Plant.” Chemical Engineering Science 254 (2022). https://doi.org/10.1016/j.ces.2022.117632. ieee: 'F. Herrmann, M. Grünewald, T. Meijer, U. Gardemann, L. Feierabend, and J. Riese, “Operating window and flexibility of a lab-scale methanation plant,” Chemical Engineering Science, vol. 254, Art. no. 117632, 2022, doi: 10.1016/j.ces.2022.117632.' mla: Herrmann, Felix, et al. “Operating Window and Flexibility of a Lab-Scale Methanation Plant.” Chemical Engineering Science, vol. 254, 117632, Elsevier BV, 2022, doi:10.1016/j.ces.2022.117632. short: F. Herrmann, M. Grünewald, T. Meijer, U. Gardemann, L. Feierabend, J. Riese, Chemical Engineering Science 254 (2022). date_created: 2023-10-04T14:15:40Z date_updated: 2024-03-08T11:39:03Z doi: 10.1016/j.ces.2022.117632 extern: '1' intvolume: ' 254' keyword: - Applied Mathematics - Industrial and Manufacturing Engineering - General Chemical Engineering - General Chemistry language: - iso: eng publication: Chemical Engineering Science publication_identifier: issn: - 0009-2509 publication_status: published publisher: Elsevier BV quality_controlled: '1' status: public title: Operating window and flexibility of a lab-scale methanation plant type: journal_article user_id: '101499' volume: 254 year: '2022' ... --- _id: '45970' 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]. ' author: - first_name: Harald full_name: Garcke, Harald last_name: Garcke - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 - first_name: Dennis full_name: Trautwein, Dennis last_name: Trautwein citation: 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 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 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} }' 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.' 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.' 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. short: H. Garcke, B. Kovács, D. Trautwein, Mathematical Models and Methods in Applied Sciences 32 (2022) 2673–2758. date_created: 2023-07-10T11:47:27Z date_updated: 2024-04-03T09:15:35Z department: - _id: '841' doi: 10.1142/s0218202522500634 intvolume: ' 32' issue: '13' keyword: - Applied Mathematics - Modeling and Simulation language: - iso: eng page: 2673-2758 publication: Mathematical Models and Methods in Applied Sciences publication_identifier: issn: - 0218-2025 - 1793-6314 publication_status: published publisher: World Scientific Pub Co Pte Ltd status: public title: Viscoelastic Cahn–Hilliard models for tumor growth type: journal_article user_id: '100441' volume: 32 year: '2022' ... --- _id: '45969' abstract: - lang: eng 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.' author: - first_name: Charles M. full_name: Elliott, Charles M. last_name: Elliott - first_name: Harald full_name: Garcke, Harald last_name: Garcke - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 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 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 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} }' 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.' 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. short: C.M. Elliott, H. Garcke, B. Kovács, Numerische Mathematik 151 (2022) 873–925. date_created: 2023-07-10T11:47:11Z date_updated: 2024-04-03T09:15:44Z department: - _id: '841' doi: 10.1007/s00211-022-01301-3 intvolume: ' 151' issue: '4' keyword: - Applied Mathematics - Computational Mathematics language: - iso: eng page: 873-925 publication: Numerische Mathematik publication_identifier: issn: - 0029-599X - 0945-3245 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces type: journal_article user_id: '100441' volume: 151 year: '2022' ... --- _id: '45963' abstract: - lang: eng 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. author: - first_name: Jörg full_name: Nick, Jörg last_name: Nick - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 - first_name: Christian full_name: Lubich, Christian last_name: Lubich 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 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 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} }' 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.' 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. short: J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 150 (2022) 1123–1164. date_created: 2023-07-10T11:44:57Z date_updated: 2024-04-03T09:18:23Z department: - _id: '841' doi: 10.1007/s00211-022-01277-0 intvolume: ' 150' issue: '4' keyword: - Applied Mathematics - Computational Mathematics language: - iso: eng page: 1123-1164 publication: Numerische Mathematik publication_identifier: issn: - 0029-599X - 0945-3245 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Time-dependent electromagnetic scattering from thin layers type: journal_article user_id: '100441' volume: 150 year: '2022' ... --- _id: '45964' abstract: - lang: eng 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." author: - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 - first_name: Buyang full_name: Li, Buyang last_name: Li citation: 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 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 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} }' 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.' 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. short: B. Kovács, B. Li, IMA Journal of Numerical Analysis (2022). date_created: 2023-07-10T11:45:14Z date_updated: 2024-04-03T09:17:59Z department: - _id: '841' doi: 10.1093/imanum/drac033 keyword: - Applied Mathematics - Computational Mathematics - General Mathematics language: - iso: eng publication: IMA Journal of Numerical Analysis publication_identifier: issn: - 0272-4979 - 1464-3642 publication_status: published publisher: Oxford University Press (OUP) status: public title: Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems type: journal_article user_id: '100441' year: '2022' ... --- _id: '45966' 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." author: - first_name: Robert full_name: Altmann, Robert last_name: Altmann - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 - first_name: Christoph full_name: Zimmer, Christoph last_name: Zimmer 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 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 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} }' 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. date_created: 2023-07-10T11:45:49Z date_updated: 2024-04-03T09:16:47Z department: - _id: '841' doi: 10.1093/imanum/drac002 intvolume: ' 43' issue: '2' keyword: - Applied Mathematics - Computational Mathematics - General Mathematics language: - iso: eng page: 950-975 publication: IMA Journal of Numerical Analysis publication_identifier: issn: - 0272-4979 - 1464-3642 publication_status: published publisher: Oxford University Press (OUP) status: public title: Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions type: journal_article user_id: '100441' volume: 43 year: '2022' ... --- _id: '45968' 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." author: - first_name: Petra full_name: Csomós, Petra last_name: Csomós - first_name: Bálint full_name: Farkas, Bálint last_name: Farkas - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 citation: 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 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 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} }' 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. 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.' 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). date_created: 2023-07-10T11:46:54Z date_updated: 2024-04-03T09:15:52Z department: - _id: '841' doi: 10.1093/imanum/drac079 keyword: - Applied Mathematics - Computational Mathematics - General Mathematics language: - iso: eng publication: IMA Journal of Numerical Analysis publication_identifier: issn: - 0272-4979 - 1464-3642 publication_status: published publisher: Oxford University Press (OUP) status: public title: Error estimates for a splitting integrator for abstract semilinear boundary coupled systems type: journal_article user_id: '100441' year: '2022' ... --- _id: '45958' 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. author: - first_name: Cedric Aaron full_name: Beschle, Cedric Aaron last_name: Beschle - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 citation: 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 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 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} }' 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.' 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.' 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. short: C.A. Beschle, B. Kovács, Numerische Mathematik 151 (2022) 1–48. date_created: 2023-07-10T11:43:44Z date_updated: 2024-04-03T09:19:34Z department: - _id: '841' doi: 10.1007/s00211-022-01280-5 intvolume: ' 151' issue: '1' keyword: - Applied Mathematics - Computational Mathematics language: - iso: eng page: 1-48 publication: Numerische Mathematik publication_identifier: issn: - 0029-599X - 0945-3245 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces type: journal_article user_id: '100441' volume: 151 year: '2022' ... --- _id: '45956' 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." author: - first_name: Jan full_name: Bohn, Jan last_name: Bohn - first_name: Michael full_name: Feischl, Michael last_name: Feischl - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 citation: 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' 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' 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} }' 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.' 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.' 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.' short: J. Bohn, M. Feischl, B. Kovács, Computational Methods in Applied Mathematics 23 (2022) 19–48. date_created: 2023-07-10T11:43:13Z date_updated: 2024-04-03T09:20:30Z department: - _id: '841' doi: 10.1515/cmam-2022-0145 intvolume: ' 23' issue: '1' keyword: - Applied Mathematics - Computational Mathematics - Numerical Analysis language: - iso: eng page: 19-48 publication: Computational Methods in Applied Mathematics publication_identifier: issn: - 1609-4840 - 1609-9389 publication_status: published publisher: Walter de Gruyter GmbH status: public title: 'FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation' type: journal_article user_id: '100441' volume: 23 year: '2022' ... --- _id: '53319' 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." author: - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: 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 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 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} }' 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.' 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. short: M. Winkler, International Mathematics Research Notices 2023 (2022) 16336–16393. date_created: 2024-04-07T12:33:44Z date_updated: 2024-04-07T12:36:06Z doi: 10.1093/imrn/rnac286 intvolume: ' 2023' issue: '19' keyword: - General Mathematics language: - iso: eng page: 16336-16393 publication: International Mathematics Research Notices publication_identifier: issn: - 1073-7928 - 1687-0247 publication_status: published publisher: Oxford University Press (OUP) status: public 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 type: journal_article user_id: '31496' volume: 2023 year: '2022' ... --- _id: '53321' 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] ' author: - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Winkler M. Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems. Communications in Contemporary Mathematics. 2022;25(10). doi:10.1142/s0219199722500626 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 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} }' 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. 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.' 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). date_created: 2024-04-07T12:35:09Z date_updated: 2024-04-07T12:35:53Z doi: 10.1142/s0219199722500626 intvolume: ' 25' issue: '10' keyword: - Applied Mathematics - General Mathematics language: - iso: eng publication: Communications in Contemporary Mathematics publication_identifier: issn: - 0219-1997 - 1793-6683 publication_status: published publisher: World Scientific Pub Co Pte Ltd status: public title: Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems type: journal_article user_id: '31496' volume: 25 year: '2022' ... --- _id: '53327' author: - first_name: Youshan full_name: Tao, Youshan last_name: Tao - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Tao Y, Winkler M. Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension. Journal of Differential Equations. 2022;343:390-418. doi:10.1016/j.jde.2022.10.022 apa: Tao, Y., & Winkler, M. (2022). Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension. Journal of Differential Equations, 343, 390–418. https://doi.org/10.1016/j.jde.2022.10.022 bibtex: '@article{Tao_Winkler_2022, title={Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension}, volume={343}, DOI={10.1016/j.jde.2022.10.022}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Tao, Youshan and Winkler, Michael}, year={2022}, pages={390–418} }' chicago: 'Tao, Youshan, and Michael Winkler. “Global Solutions to a Keller-Segel-Consumption System Involving Singularly Signal-Dependent Motilities in Domains of Arbitrary Dimension.” Journal of Differential Equations 343 (2022): 390–418. https://doi.org/10.1016/j.jde.2022.10.022.' ieee: 'Y. Tao and M. Winkler, “Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension,” Journal of Differential Equations, vol. 343, pp. 390–418, 2022, doi: 10.1016/j.jde.2022.10.022.' mla: Tao, Youshan, and Michael Winkler. “Global Solutions to a Keller-Segel-Consumption System Involving Singularly Signal-Dependent Motilities in Domains of Arbitrary Dimension.” Journal of Differential Equations, vol. 343, Elsevier BV, 2022, pp. 390–418, doi:10.1016/j.jde.2022.10.022. short: Y. Tao, M. Winkler, Journal of Differential Equations 343 (2022) 390–418. date_created: 2024-04-07T12:42:28Z date_updated: 2024-04-07T12:42:32Z doi: 10.1016/j.jde.2022.10.022 intvolume: ' 343' keyword: - Analysis - Applied Mathematics language: - iso: eng page: 390-418 publication: Journal of Differential Equations publication_identifier: issn: - 0022-0396 publication_status: published publisher: Elsevier BV status: public title: Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension type: journal_article user_id: '31496' volume: 343 year: '2022' ... --- _id: '53325' article_number: '113153' author: - first_name: Laurent full_name: Desvillettes, Laurent last_name: Desvillettes - first_name: Philippe full_name: Laurençot, Philippe last_name: Laurençot - first_name: Ariane full_name: Trescases, Ariane last_name: Trescases - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Desvillettes L, Laurençot P, Trescases A, Winkler M. Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing. Nonlinear Analysis. 2022;226. doi:10.1016/j.na.2022.113153 apa: Desvillettes, L., Laurençot, P., Trescases, A., & Winkler, M. (2022). Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing. Nonlinear Analysis, 226, Article 113153. https://doi.org/10.1016/j.na.2022.113153 bibtex: '@article{Desvillettes_Laurençot_Trescases_Winkler_2022, title={Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing}, volume={226}, DOI={10.1016/j.na.2022.113153}, number={113153}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Desvillettes, Laurent and Laurençot, Philippe and Trescases, Ariane and Winkler, Michael}, year={2022} }' chicago: Desvillettes, Laurent, Philippe Laurençot, Ariane Trescases, and Michael Winkler. “Weak Solutions to Triangular Cross Diffusion Systems Modeling Chemotaxis with Local Sensing.” Nonlinear Analysis 226 (2022). https://doi.org/10.1016/j.na.2022.113153. ieee: 'L. Desvillettes, P. Laurençot, A. Trescases, and M. Winkler, “Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing,” Nonlinear Analysis, vol. 226, Art. no. 113153, 2022, doi: 10.1016/j.na.2022.113153.' mla: Desvillettes, Laurent, et al. “Weak Solutions to Triangular Cross Diffusion Systems Modeling Chemotaxis with Local Sensing.” Nonlinear Analysis, vol. 226, 113153, Elsevier BV, 2022, doi:10.1016/j.na.2022.113153. short: L. Desvillettes, P. Laurençot, A. Trescases, M. Winkler, Nonlinear Analysis 226 (2022). date_created: 2024-04-07T12:41:15Z date_updated: 2024-04-07T12:41:20Z doi: 10.1016/j.na.2022.113153 intvolume: ' 226' keyword: - Applied Mathematics - Analysis language: - iso: eng publication: Nonlinear Analysis publication_identifier: issn: - 0362-546X publication_status: published publisher: Elsevier BV status: public title: Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing type: journal_article user_id: '31496' volume: 226 year: '2022' ... --- _id: '53331' abstract: - lang: eng text: "In a ball

$\\Omega \\subset \\mathbb {R}^{n}$

with

$n\\ge 2$

, the chemotaxis system\r\n

\\[ \\left\\{ \\begin{array}{@{}l} u_t = \\nabla \\cdot \\big( D(u)\\nabla u\\big) + \\nabla\\cdot \\big(\\dfrac{u}{v} \\nabla v\\big), \\\\ 0=\\Delta v - uv \\end{array} \\right. \\]

is considered along with no-flux boundary conditions for

$u$

and with prescribed constant positive Dirichlet boundary data for

$v$

. It is shown that if

$D\\in C^{3}([0,\\infty ))$

is such that

$0< D(\\xi ) \\le {K_D} (\\xi +1)^{-\\alpha }$

for all

$\\xi >0$

with some

${K_D}>0$

and

$\\alpha >0$

, then for all initial data from a considerably large set of radial functions on

$\\Omega$

, the corresponding initial-boundary value problem admits a solution blowing up in finite time." author: - first_name: Yulan full_name: Wang, Yulan last_name: Wang - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: 'Wang Y, Winkler M. Finite-time blow-up in a repulsive chemotaxis-consumption system. Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 2022;153(4):1150-1166. doi:10.1017/prm.2022.39' apa: 'Wang, Y., & Winkler, M. (2022). Finite-time blow-up in a repulsive chemotaxis-consumption system. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 153(4), 1150–1166. https://doi.org/10.1017/prm.2022.39' bibtex: '@article{Wang_Winkler_2022, title={Finite-time blow-up in a repulsive chemotaxis-consumption system}, volume={153}, DOI={10.1017/prm.2022.39}, number={4}, journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics}, publisher={Cambridge University Press (CUP)}, author={Wang, Yulan and Winkler, Michael}, year={2022}, pages={1150–1166} }' chicago: 'Wang, Yulan, and Michael Winkler. “Finite-Time Blow-up in a Repulsive Chemotaxis-Consumption System.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics 153, no. 4 (2022): 1150–66. https://doi.org/10.1017/prm.2022.39.' ieee: 'Y. Wang and M. Winkler, “Finite-time blow-up in a repulsive chemotaxis-consumption system,” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 153, no. 4, pp. 1150–1166, 2022, doi: 10.1017/prm.2022.39.' mla: 'Wang, Yulan, and Michael Winkler. “Finite-Time Blow-up in a Repulsive Chemotaxis-Consumption System.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 153, no. 4, Cambridge University Press (CUP), 2022, pp. 1150–66, doi:10.1017/prm.2022.39.' short: 'Y. Wang, M. Winkler, Proceedings of the Royal Society of Edinburgh: Section A Mathematics 153 (2022) 1150–1166.' date_created: 2024-04-07T12:44:26Z date_updated: 2024-04-07T12:44:30Z doi: 10.1017/prm.2022.39 intvolume: ' 153' issue: '4' keyword: - General Mathematics language: - iso: eng page: 1150-1166 publication: 'Proceedings of the Royal Society of Edinburgh: Section A Mathematics' publication_identifier: issn: - 0308-2105 - 1473-7124 publication_status: published publisher: Cambridge University Press (CUP) status: public title: Finite-time blow-up in a repulsive chemotaxis-consumption system type: journal_article user_id: '31496' volume: 153 year: '2022' ... --- _id: '53344' abstract: - lang: eng text: ' A no-flux initial-boundary value problem for the cross-diffusion system [Formula: see text] is considered in smoothly bounded domains [Formula: see text] with [Formula: see text]. It is shown that whenever [Formula: see text] is positive on [Formula: see text] and such that [Formula: see text] for some [Formula: see text], for all suitably regular positive initial data a global very weak solution, particularly preserving mass in its first component, can be constructed. This extends previous results which either concentrate on non-degenerate analogs, or are restricted to the special case [Formula: see text]. To appropriately cope with the considerably stronger cross-degeneracies thus allowed through [Formula: see text] when [Formula: see text] is large, in its core part the analysis relies on the use of the Moser–Trudinger inequality in controlling the respective diffusion rates [Formula: see text] from below. ' author: - first_name: Michael full_name: Winkler, Michael last_name: Winkler citation: ama: Winkler M. Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model. Bulletin of Mathematical Sciences. 2022;13(02). doi:10.1142/s1664360722500126 apa: Winkler, M. (2022). Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model. Bulletin of Mathematical Sciences, 13(02). https://doi.org/10.1142/s1664360722500126 bibtex: '@article{Winkler_2022, title={Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model}, volume={13}, DOI={10.1142/s1664360722500126}, number={02}, journal={Bulletin of Mathematical Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Winkler, Michael}, year={2022} }' chicago: Winkler, Michael. “Application of the Moser–Trudinger Inequality in the Construction of Global Solutions to a Strongly Degenerate Migration Model.” Bulletin of Mathematical Sciences 13, no. 02 (2022). https://doi.org/10.1142/s1664360722500126. ieee: 'M. Winkler, “Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model,” Bulletin of Mathematical Sciences, vol. 13, no. 02, 2022, doi: 10.1142/s1664360722500126.' mla: Winkler, Michael. “Application of the Moser–Trudinger Inequality in the Construction of Global Solutions to a Strongly Degenerate Migration Model.” Bulletin of Mathematical Sciences, vol. 13, no. 02, World Scientific Pub Co Pte Ltd, 2022, doi:10.1142/s1664360722500126. short: M. Winkler, Bulletin of Mathematical Sciences 13 (2022). date_created: 2024-04-07T12:55:07Z date_updated: 2024-04-07T12:55:11Z doi: 10.1142/s1664360722500126 intvolume: ' 13' issue: '02' keyword: - General Mathematics language: - iso: eng publication: Bulletin of Mathematical Sciences publication_identifier: issn: - 1664-3607 - 1664-3615 publication_status: published publisher: World Scientific Pub Co Pte Ltd status: public title: Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model type: journal_article user_id: '31496' volume: 13 year: '2022' ... --- _id: '44689' abstract: - lang: eng text: AbstractEven in the digital age, learning mathematics at an academic level still requires much reading of mathematical text. Research has shown that reading mathematical text requires readers to engage with all the structures of the book and with its pedagogical voice, making connections, and plausible reasoning. Specific practices and strategies that support the close reading of mathematical text have been suggested; however, descriptions and empirical evaluations of materials designed to support these activities are rare. We present the design and first evaluation cycle of materials developed in a design research project that aims to scaffold close reading of mathematical text. The materials were designed and evaluated in a German university course on elementary geometry for first-year teacher education students who study mathematics to become primary teachers. The reading strategies were explained and modeled for students in reading-strategy videos. Additionally, close reading of mathematical text was scaffolded by close-reading tasks and homework tasks and problems that build on the reading strategies and were specifically designed to foster understanding of the mathematical text. Survey data were collected from 296 students to evaluate their use of and attitude toward the different materials. The quantitative results indicate that students used the materials and were generally able to learn the course content by themselves. From all provided materials, they found the close-reading tasks most helpful. A qualitative analysis of answers to open questions revealed issues with different materials, particularly with the script, and requests for additional materials. The issues with the script were categorized inductively. The categories are presented as a qualitative result of the study and discussed. author: - first_name: Sebastian full_name: Rezat, Sebastian id: '31132' last_name: Rezat - first_name: Sara Naseem full_name: Malik, Sara Naseem id: '38640' last_name: Malik - first_name: Markus full_name: Leifeld, Markus last_name: Leifeld citation: ama: 'Rezat S, Malik SN, Leifeld M. Scaffolding Close Reading of Mathematical Text in Pre-service Primary Teacher Education at the Tertiary Level: Design and Evaluation. International Journal of Science and Mathematics Education. 2022;20(S1):215-236. doi:10.1007/s10763-022-10309-y' apa: 'Rezat, S., Malik, S. N., & Leifeld, M. (2022). Scaffolding Close Reading of Mathematical Text in Pre-service Primary Teacher Education at the Tertiary Level: Design and Evaluation. International Journal of Science and Mathematics Education, 20(S1), 215–236. https://doi.org/10.1007/s10763-022-10309-y' bibtex: '@article{Rezat_Malik_Leifeld_2022, title={Scaffolding Close Reading of Mathematical Text in Pre-service Primary Teacher Education at the Tertiary Level: Design and Evaluation}, volume={20}, DOI={10.1007/s10763-022-10309-y}, number={S1}, journal={International Journal of Science and Mathematics Education}, publisher={Springer}, author={Rezat, Sebastian and Malik, Sara Naseem and Leifeld, Markus}, year={2022}, pages={215–236} }' chicago: 'Rezat, Sebastian, Sara Naseem Malik, and Markus Leifeld. “Scaffolding Close Reading of Mathematical Text in Pre-Service Primary Teacher Education at the Tertiary Level: Design and Evaluation.” International Journal of Science and Mathematics Education 20, no. S1 (2022): 215–36. https://doi.org/10.1007/s10763-022-10309-y.' ieee: 'S. Rezat, S. N. Malik, and M. Leifeld, “Scaffolding Close Reading of Mathematical Text in Pre-service Primary Teacher Education at the Tertiary Level: Design and Evaluation,” International Journal of Science and Mathematics Education, vol. 20, no. S1, pp. 215–236, 2022, doi: 10.1007/s10763-022-10309-y.' mla: 'Rezat, Sebastian, et al. “Scaffolding Close Reading of Mathematical Text in Pre-Service Primary Teacher Education at the Tertiary Level: Design and Evaluation.” International Journal of Science and Mathematics Education, vol. 20, no. S1, Springer, 2022, pp. 215–36, doi:10.1007/s10763-022-10309-y.' short: S. Rezat, S.N. Malik, M. Leifeld, International Journal of Science and Mathematics Education 20 (2022) 215–236. date_created: 2023-05-09T14:03:15Z date_updated: 2024-04-18T08:22:47Z department: - _id: '360' doi: 10.1007/s10763-022-10309-y intvolume: ' 20' issue: S1 keyword: - General Mathematics - Education language: - iso: eng page: 215-236 publication: International Journal of Science and Mathematics Education publication_identifier: issn: - 1571-0068 - 1573-1774 publication_status: published publisher: Springer quality_controlled: '1' status: public title: 'Scaffolding Close Reading of Mathematical Text in Pre-service Primary Teacher Education at the Tertiary Level: Design and Evaluation' type: journal_article user_id: '31132' volume: 20 year: '2022' ... --- _id: '35685' author: - first_name: Michael full_name: Liebendörfer, Michael id: '30933' last_name: Liebendörfer orcid: 0000-0001-9887-2074 - first_name: Robin full_name: Göller, Robin last_name: Göller - first_name: Lara full_name: Gildehaus, Lara last_name: Gildehaus - first_name: Jörg full_name: Kortemeyer, Jörg last_name: Kortemeyer - first_name: Rolf full_name: Biehler, Rolf id: '16274' last_name: Biehler - first_name: Reinhard full_name: Hochmuth, Reinhard last_name: Hochmuth - first_name: Laura full_name: Ostsieker, Laura last_name: Ostsieker - first_name: Jana full_name: Rode, Jana last_name: Rode - first_name: Niclas full_name: Schaper, Niclas last_name: Schaper citation: ama: Liebendörfer M, Göller R, Gildehaus L, et al. The role of learning strategies for performance in mathematics courses for engineers. International Journal of Mathematical Education in Science and Technology. 2022;53(5):1133-1152. doi:10.1080/0020739x.2021.2023772 apa: Liebendörfer, M., Göller, R., Gildehaus, L., Kortemeyer, J., Biehler, R., Hochmuth, R., Ostsieker, L., Rode, J., & Schaper, N. (2022). The role of learning strategies for performance in mathematics courses for engineers. International Journal of Mathematical Education in Science and Technology, 53(5), 1133–1152. https://doi.org/10.1080/0020739x.2021.2023772 bibtex: '@article{Liebendörfer_Göller_Gildehaus_Kortemeyer_Biehler_Hochmuth_Ostsieker_Rode_Schaper_2022, title={The role of learning strategies for performance in mathematics courses for engineers}, volume={53}, DOI={10.1080/0020739x.2021.2023772}, number={5}, journal={International Journal of Mathematical Education in Science and Technology}, publisher={Informa UK Limited}, author={Liebendörfer, Michael and Göller, Robin and Gildehaus, Lara and Kortemeyer, Jörg and Biehler, Rolf and Hochmuth, Reinhard and Ostsieker, Laura and Rode, Jana and Schaper, Niclas}, year={2022}, pages={1133–1152} }' chicago: 'Liebendörfer, Michael, Robin Göller, Lara Gildehaus, Jörg Kortemeyer, Rolf Biehler, Reinhard Hochmuth, Laura Ostsieker, Jana Rode, and Niclas Schaper. “The Role of Learning Strategies for Performance in Mathematics Courses for Engineers.” International Journal of Mathematical Education in Science and Technology 53, no. 5 (2022): 1133–52. https://doi.org/10.1080/0020739x.2021.2023772.' ieee: 'M. Liebendörfer et al., “The role of learning strategies for performance in mathematics courses for engineers,” International Journal of Mathematical Education in Science and Technology, vol. 53, no. 5, pp. 1133–1152, 2022, doi: 10.1080/0020739x.2021.2023772.' mla: Liebendörfer, Michael, et al. “The Role of Learning Strategies for Performance in Mathematics Courses for Engineers.” International Journal of Mathematical Education in Science and Technology, vol. 53, no. 5, Informa UK Limited, 2022, pp. 1133–52, doi:10.1080/0020739x.2021.2023772. short: M. Liebendörfer, R. Göller, L. Gildehaus, J. Kortemeyer, R. Biehler, R. Hochmuth, L. Ostsieker, J. Rode, N. Schaper, International Journal of Mathematical Education in Science and Technology 53 (2022) 1133–1152. date_created: 2023-01-10T08:56:30Z date_updated: 2024-04-18T10:08:30Z department: - _id: '363' - _id: '625' doi: 10.1080/0020739x.2021.2023772 intvolume: ' 53' issue: '5' keyword: - Applied Mathematics - Education - Mathematics (miscellaneous) language: - iso: eng page: 1133-1152 publication: International Journal of Mathematical Education in Science and Technology publication_identifier: issn: - 0020-739X - 1464-5211 publication_status: published publisher: Informa UK Limited status: public title: The role of learning strategies for performance in mathematics courses for engineers type: journal_article user_id: '37888' volume: 53 year: '2022' ... --- _id: '45849' abstract: - lang: eng text: 'AbstractDependence Logic was introduced by Jouko Väänänen in 2007. We study a propositional variant of this logic(PDL)and investigate a variety of parameterisations with respect to central decision problems. The model checking problem (MC) ofPDLisNP-complete (Ebbing and Lohmann, SOFSEM 2012). The subject of this research is to identify a list of parameterisations (formula-size, formula-depth, treewidth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) which classically is known to beNP-complete as well (Lohmann and Vollmer, Studia Logica 2013). There we are presenting a different picture: under team-size, or dep-arity SAT isparaNP-complete whereas under all other mentioned parameters the problem isFPT. Finally, we introduce a variant of the satisfiability problem, asking for a team of a given size, and show for this problem an almost complete picture.' author: - first_name: Yasir full_name: Mahmood, Yasir id: '99353' last_name: Mahmood - first_name: Arne full_name: Meier, Arne last_name: Meier citation: ama: Mahmood Y, Meier A. Parameterised complexity of model checking and satisfiability in propositional dependence logic. Annals of Mathematics and Artificial Intelligence. 2022;90(2-3):271-296. doi:10.1007/s10472-021-09730-w apa: Mahmood, Y., & Meier, A. (2022). Parameterised complexity of model checking and satisfiability in propositional dependence logic. Annals of Mathematics and Artificial Intelligence, 90(2–3), 271–296. https://doi.org/10.1007/s10472-021-09730-w bibtex: '@article{Mahmood_Meier_2022, title={Parameterised complexity of model checking and satisfiability in propositional dependence logic}, volume={90}, DOI={10.1007/s10472-021-09730-w}, number={2–3}, journal={Annals of Mathematics and Artificial Intelligence}, publisher={Springer Science and Business Media LLC}, author={Mahmood, Yasir and Meier, Arne}, year={2022}, pages={271–296} }' chicago: 'Mahmood, Yasir, and Arne Meier. “Parameterised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic.” Annals of Mathematics and Artificial Intelligence 90, no. 2–3 (2022): 271–96. https://doi.org/10.1007/s10472-021-09730-w.' ieee: 'Y. Mahmood and A. Meier, “Parameterised complexity of model checking and satisfiability in propositional dependence logic,” Annals of Mathematics and Artificial Intelligence, vol. 90, no. 2–3, pp. 271–296, 2022, doi: 10.1007/s10472-021-09730-w.' mla: Mahmood, Yasir, and Arne Meier. “Parameterised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic.” Annals of Mathematics and Artificial Intelligence, vol. 90, no. 2–3, Springer Science and Business Media LLC, 2022, pp. 271–96, doi:10.1007/s10472-021-09730-w. short: Y. Mahmood, A. Meier, Annals of Mathematics and Artificial Intelligence 90 (2022) 271–296. date_created: 2023-07-03T11:45:39Z date_updated: 2024-06-04T16:06:59Z doi: 10.1007/s10472-021-09730-w extern: '1' intvolume: ' 90' issue: 2-3 keyword: - Applied Mathematics - Artificial Intelligence language: - iso: eng page: 271-296 publication: Annals of Mathematics and Artificial Intelligence publication_identifier: issn: - 1012-2443 - 1573-7470 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Parameterised complexity of model checking and satisfiability in propositional dependence logic type: journal_article user_id: '99353' volume: 90 year: '2022' ... --- _id: '34264' abstract: - lang: eng text: In industrial x-ray computed tomography (CT), the application of more complex scan paths in comparison to the typical circular trajectory (${360}^{\circ}$ rotation of the measurement object) can extend the potential of CT. One way to enable such 3D scan trajectories is to use a 6-degrees-of-freedom (DOF) object manipulator system. In our case, a hexapod is mounted on top of the rotary table of a commercial CT scanner. This allows for adaptive tilting of the measurement object during the scan. For high accuracy, the geometry calibration of such setups is typically done using the x-ray projections of a calibrated multi-sphere object. Contrary to this, here, we demonstrate a procedure that is based on only a single sphere and can therefore experimentally be implemented with low effort. Using the intrinsic geometry parameters of the CT device as prior information, the hexapod coordinate system with respect to the CT machine coordinate system is determined by means of a one-step optimization approach. The resulting parameters are used to calculate projection matrices that enable the volume reconstruction for 3D scan trajectories. The method is validated using simulated x-ray images and experimental investigations including dimensional measurements. For the used setup, geometric measurement results for 3D scan trajectories that are calibrated with the presented method show in sum increased errors compared to the circular scans. A limited pose accuracy of the manipulator system is discussed as a potential cause. The results nevertheless indicate that the presented method is generally feasible for dimensional CT measurements provided that the pose accuracy is sufficient. The calibration procedure can therefore be a low-cost and easier to implement alternative compared to trajectory calibration methods based on multi-sphere objects, but with a tendency towards lower measurement accuracy. The methodology can in principle be transferred to different setups with 6-DOF manipulator systems, e.g. C-arm CT devices with a robot arm. article_number: '015403' author: - first_name: Lorenz full_name: Butzhammer, Lorenz last_name: Butzhammer - first_name: Andreas Michael full_name: Müller, Andreas Michael last_name: Müller - first_name: Tino full_name: Hausotte, Tino last_name: Hausotte citation: ama: Butzhammer L, Müller AM, Hausotte T. Calibration of 3D scan trajectories for an industrial computed tomography setup with 6-DOF object manipulator system using a single sphere. Measurement Science and Technology. 2022;34(1). doi:10.1088/1361-6501/ac9856 apa: Butzhammer, L., Müller, A. M., & Hausotte, T. (2022). Calibration of 3D scan trajectories for an industrial computed tomography setup with 6-DOF object manipulator system using a single sphere. Measurement Science and Technology, 34(1), Article 015403. https://doi.org/10.1088/1361-6501/ac9856 bibtex: '@article{Butzhammer_Müller_Hausotte_2022, title={Calibration of 3D scan trajectories for an industrial computed tomography setup with 6-DOF object manipulator system using a single sphere}, volume={34}, DOI={10.1088/1361-6501/ac9856}, number={1015403}, journal={Measurement Science and Technology}, publisher={IOP Publishing}, author={Butzhammer, Lorenz and Müller, Andreas Michael and Hausotte, Tino}, year={2022} }' chicago: Butzhammer, Lorenz, Andreas Michael Müller, and Tino Hausotte. “Calibration of 3D Scan Trajectories for an Industrial Computed Tomography Setup with 6-DOF Object Manipulator System Using a Single Sphere.” Measurement Science and Technology 34, no. 1 (2022). https://doi.org/10.1088/1361-6501/ac9856. ieee: 'L. Butzhammer, A. M. Müller, and T. Hausotte, “Calibration of 3D scan trajectories for an industrial computed tomography setup with 6-DOF object manipulator system using a single sphere,” Measurement Science and Technology, vol. 34, no. 1, Art. no. 015403, 2022, doi: 10.1088/1361-6501/ac9856.' mla: Butzhammer, Lorenz, et al. “Calibration of 3D Scan Trajectories for an Industrial Computed Tomography Setup with 6-DOF Object Manipulator System Using a Single Sphere.” Measurement Science and Technology, vol. 34, no. 1, 015403, IOP Publishing, 2022, doi:10.1088/1361-6501/ac9856. short: L. Butzhammer, A.M. Müller, T. Hausotte, Measurement Science and Technology 34 (2022). date_created: 2022-12-07T10:46:14Z date_updated: 2023-01-13T14:34:31Z department: - _id: '630' doi: 10.1088/1361-6501/ac9856 intvolume: ' 34' issue: '1' keyword: - Applied Mathematics - Instrumentation - Engineering (miscellaneous) language: - iso: eng main_file_link: - open_access: '1' url: https://iopscience.iop.org/article/10.1088/1361-6501/ac9856 oa: '1' project: - _id: '130' grant_number: '418701707' name: 'TRR 285: TRR 285' - _id: '133' name: 'TRR 285 - C: TRR 285 - Project Area C' - _id: '149' name: 'TRR 285 – C05: TRR 285 - Subproject C05' publication: Measurement Science and Technology publication_identifier: issn: - 0957-0233 - 1361-6501 publication_status: published publisher: IOP Publishing status: public title: Calibration of 3D scan trajectories for an industrial computed tomography setup with 6-DOF object manipulator system using a single sphere type: journal_article user_id: '7850' volume: 34 year: '2022' ... --- _id: '35206' author: - first_name: Bernard full_name: Bonnard, Bernard last_name: Bonnard - first_name: Jérémy full_name: Rouot, Jérémy last_name: Rouot - first_name: Boris Edgar full_name: Wembe Moafo, Boris Edgar id: '95394' last_name: Wembe Moafo citation: ama: Bonnard B, Rouot J, Wembe Moafo BE. Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies. Mathematical Control and Related Fields. 2022;0(0):0-0. doi:10.3934/mcrf.2022052 apa: Bonnard, B., Rouot, J., & Wembe Moafo, B. E. (2022). Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies. Mathematical Control and Related Fields, 0(0), 0–0. https://doi.org/10.3934/mcrf.2022052 bibtex: '@article{Bonnard_Rouot_Wembe Moafo_2022, title={Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies}, volume={0}, DOI={10.3934/mcrf.2022052}, number={0}, journal={Mathematical Control and Related Fields}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Bonnard, Bernard and Rouot, Jérémy and Wembe Moafo, Boris Edgar}, year={2022}, pages={0–0} }' chicago: 'Bonnard, Bernard, Jérémy Rouot, and Boris Edgar Wembe Moafo. “Accessibility Properties of Abnormal Geodesics in Optimal Control Illustrated by Two Case Studies.” Mathematical Control and Related Fields 0, no. 0 (2022): 0–0. https://doi.org/10.3934/mcrf.2022052.' ieee: 'B. Bonnard, J. Rouot, and B. E. Wembe Moafo, “Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies,” Mathematical Control and Related Fields, vol. 0, no. 0, pp. 0–0, 2022, doi: 10.3934/mcrf.2022052.' mla: Bonnard, Bernard, et al. “Accessibility Properties of Abnormal Geodesics in Optimal Control Illustrated by Two Case Studies.” Mathematical Control and Related Fields, vol. 0, no. 0, American Institute of Mathematical Sciences (AIMS), 2022, pp. 0–0, doi:10.3934/mcrf.2022052. short: B. Bonnard, J. Rouot, B.E. Wembe Moafo, Mathematical Control and Related Fields 0 (2022) 0–0. date_created: 2023-01-04T10:26:56Z date_updated: 2023-01-16T12:07:51Z doi: 10.3934/mcrf.2022052 issue: '0' keyword: - Applied Mathematics - Control and Optimization - General Medicine language: - iso: eng page: 0-0 publication: Mathematical Control and Related Fields publication_identifier: issn: - 2156-8472 - 2156-8499 publication_status: published publisher: American Institute of Mathematical Sciences (AIMS) status: public title: Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies type: journal_article user_id: '95394' volume: '0' year: '2022' ...