[{"type":"journal_article","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"date_created":"2026-01-15T10:09:43Z","publication":"Annali di Matematica Pura ed Applicata (1923 -)","citation":{"mla":"Black, Tobias. “Refining Hölder Regularity Theory in Degenerate Drift-Diffusion Equations.” <i>Annali Di Matematica Pura Ed Applicata (1923 -)</i>, Springer Science and Business Media LLC, 2026, doi:<a href=\"https://doi.org/10.1007/s10231-025-01642-4\">10.1007/s10231-025-01642-4</a>.","bibtex":"@article{Black_2026, title={Refining Hölder regularity theory in degenerate drift-diffusion equations}, DOI={<a href=\"https://doi.org/10.1007/s10231-025-01642-4\">10.1007/s10231-025-01642-4</a>}, journal={Annali di Matematica Pura ed Applicata (1923 -)}, publisher={Springer Science and Business Media LLC}, author={Black, Tobias}, year={2026} }","ama":"Black T. Refining Hölder regularity theory in degenerate drift-diffusion equations. <i>Annali di Matematica Pura ed Applicata (1923 -)</i>. Published online 2026. doi:<a href=\"https://doi.org/10.1007/s10231-025-01642-4\">10.1007/s10231-025-01642-4</a>","ieee":"T. Black, “Refining Hölder regularity theory in degenerate drift-diffusion equations,” <i>Annali di Matematica Pura ed Applicata (1923 -)</i>, 2026, doi: <a href=\"https://doi.org/10.1007/s10231-025-01642-4\">10.1007/s10231-025-01642-4</a>.","apa":"Black, T. (2026). Refining Hölder regularity theory in degenerate drift-diffusion equations. <i>Annali Di Matematica Pura Ed Applicata (1923 -)</i>. <a href=\"https://doi.org/10.1007/s10231-025-01642-4\">https://doi.org/10.1007/s10231-025-01642-4</a>","chicago":"Black, Tobias. “Refining Hölder Regularity Theory in Degenerate Drift-Diffusion Equations.” <i>Annali Di Matematica Pura Ed Applicata (1923 -)</i>, 2026. <a href=\"https://doi.org/10.1007/s10231-025-01642-4\">https://doi.org/10.1007/s10231-025-01642-4</a>.","short":"T. Black, Annali Di Matematica Pura Ed Applicata (1923 -) (2026)."},"user_id":"23686","doi":"10.1007/s10231-025-01642-4","language":[{"iso":"eng"}],"_id":"63621","publisher":"Springer Science and Business Media LLC","publication_status":"published","date_updated":"2026-01-15T10:10:58Z","title":"Refining Hölder regularity theory in degenerate drift-diffusion equations","year":"2026","status":"public","author":[{"id":"23686","orcid":"0000-0001-9963-0800","last_name":"Black","first_name":"Tobias","full_name":"Black, Tobias"}],"publication_identifier":{"issn":["0373-3114","1618-1891"]}},{"doi":"10.1007/s00028-025-01163-w","language":[{"iso":"eng"}],"article_number":"24","intvolume":"        26","date_updated":"2026-01-20T14:14:50Z","publication_status":"published","author":[{"full_name":"Black, Tobias","last_name":"Black","orcid":"0000-0001-9963-0800","first_name":"Tobias","id":"23686"},{"last_name":"Kohatsu","first_name":"Shohei","full_name":"Kohatsu, Shohei"},{"first_name":"Duan","last_name":"Wu","full_name":"Wu, Duan"}],"publication_identifier":{"issn":["1424-3199","1424-3202"]},"year":"2026","title":"Global solvability and large-time behavior in a doubly degenerate migration model involving saturated signal consumption","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"type":"journal_article","date_created":"2026-01-20T14:13:53Z","publication":"Journal of Evolution Equations","issue":"1","volume":26,"user_id":"23686","publisher":"Springer Science and Business Media LLC","_id":"63672","status":"public","citation":{"ama":"Black T, Kohatsu S, Wu D. Global solvability and large-time behavior in a doubly degenerate migration model involving saturated signal consumption. <i>Journal of Evolution Equations</i>. 2026;26(1). doi:<a href=\"https://doi.org/10.1007/s00028-025-01163-w\">10.1007/s00028-025-01163-w</a>","bibtex":"@article{Black_Kohatsu_Wu_2026, title={Global solvability and large-time behavior in a doubly degenerate migration model involving saturated signal consumption}, volume={26}, DOI={<a href=\"https://doi.org/10.1007/s00028-025-01163-w\">10.1007/s00028-025-01163-w</a>}, number={124}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Black, Tobias and Kohatsu, Shohei and Wu, Duan}, year={2026} }","mla":"Black, Tobias, et al. “Global Solvability and Large-Time Behavior in a Doubly Degenerate Migration Model Involving Saturated Signal Consumption.” <i>Journal of Evolution Equations</i>, vol. 26, no. 1, 24, Springer Science and Business Media LLC, 2026, doi:<a href=\"https://doi.org/10.1007/s00028-025-01163-w\">10.1007/s00028-025-01163-w</a>.","chicago":"Black, Tobias, Shohei Kohatsu, and Duan Wu. “Global Solvability and Large-Time Behavior in a Doubly Degenerate Migration Model Involving Saturated Signal Consumption.” <i>Journal of Evolution Equations</i> 26, no. 1 (2026). <a href=\"https://doi.org/10.1007/s00028-025-01163-w\">https://doi.org/10.1007/s00028-025-01163-w</a>.","short":"T. Black, S. Kohatsu, D. Wu, Journal of Evolution Equations 26 (2026).","apa":"Black, T., Kohatsu, S., &#38; Wu, D. (2026). Global solvability and large-time behavior in a doubly degenerate migration model involving saturated signal consumption. <i>Journal of Evolution Equations</i>, <i>26</i>(1), Article 24. <a href=\"https://doi.org/10.1007/s00028-025-01163-w\">https://doi.org/10.1007/s00028-025-01163-w</a>","ieee":"T. Black, S. Kohatsu, and D. Wu, “Global solvability and large-time behavior in a doubly degenerate migration model involving saturated signal consumption,” <i>Journal of Evolution Equations</i>, vol. 26, no. 1, Art. no. 24, 2026, doi: <a href=\"https://doi.org/10.1007/s00028-025-01163-w\">10.1007/s00028-025-01163-w</a>."}},{"author":[{"last_name":"Black","orcid":"0000-0001-9963-0800","first_name":"Tobias","full_name":"Black, Tobias","id":"23686"},{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}],"publication_identifier":{"issn":["2163-2480"]},"title":"Global solutions and large time stabilization in a model for thermoacoustics in a standard linear solid","year":"2026","intvolume":"        25","date_updated":"2026-08-11T09:52:50Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.3934/eect.2026091","issue":"0","publication":"Evolution Equations and Control Theory","date_created":"2026-08-11T09:50:10Z","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"type":"journal_article","status":"public","_id":"66694","publisher":"American Institute of Mathematical Sciences (AIMS)","page":"278-308","volume":25,"user_id":"23686","citation":{"apa":"Black, T., &#38; Winkler, M. (2026). Global solutions and large time stabilization in a model for thermoacoustics in a standard linear solid. <i>Evolution Equations and Control Theory</i>, <i>25</i>(0), 278–308. <a href=\"https://doi.org/10.3934/eect.2026091\">https://doi.org/10.3934/eect.2026091</a>","ieee":"T. Black and M. Winkler, “Global solutions and large time stabilization in a model for thermoacoustics in a standard linear solid,” <i>Evolution Equations and Control Theory</i>, vol. 25, no. 0, pp. 278–308, 2026, doi: <a href=\"https://doi.org/10.3934/eect.2026091\">10.3934/eect.2026091</a>.","chicago":"Black, Tobias, and Michael Winkler. “Global Solutions and Large Time Stabilization in a Model for Thermoacoustics in a Standard Linear Solid.” <i>Evolution Equations and Control Theory</i> 25, no. 0 (2026): 278–308. <a href=\"https://doi.org/10.3934/eect.2026091\">https://doi.org/10.3934/eect.2026091</a>.","short":"T. Black, M. Winkler, Evolution Equations and Control Theory 25 (2026) 278–308.","mla":"Black, Tobias, and Michael Winkler. “Global Solutions and Large Time Stabilization in a Model for Thermoacoustics in a Standard Linear Solid.” <i>Evolution Equations and Control Theory</i>, vol. 25, no. 0, American Institute of Mathematical Sciences (AIMS), 2026, pp. 278–308, doi:<a href=\"https://doi.org/10.3934/eect.2026091\">10.3934/eect.2026091</a>.","ama":"Black T, Winkler M. Global solutions and large time stabilization in a model for thermoacoustics in a standard linear solid. <i>Evolution Equations and Control Theory</i>. 2026;25(0):278-308. doi:<a href=\"https://doi.org/10.3934/eect.2026091\">10.3934/eect.2026091</a>","bibtex":"@article{Black_Winkler_2026, title={Global solutions and large time stabilization in a model for thermoacoustics in a standard linear solid}, volume={25}, DOI={<a href=\"https://doi.org/10.3934/eect.2026091\">10.3934/eect.2026091</a>}, number={0}, journal={Evolution Equations and Control Theory}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Black, Tobias and Winkler, Michael}, year={2026}, pages={278–308} }"}},{"date_created":"2024-11-08T13:28:04Z","type":"journal_article","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"publication":"Applied Mathematics Letters","citation":{"chicago":"Black, Tobias. “Absence of Dead-Core Formations in Chemotaxis Systems with Degenerate Diffusion.” <i>Applied Mathematics Letters</i> 161 (2025). <a href=\"https://doi.org/10.1016/j.aml.2024.109361\">https://doi.org/10.1016/j.aml.2024.109361</a>.","short":"T. Black, Applied Mathematics Letters 161 (2025).","apa":"Black, T. (2025). Absence of dead-core formations in chemotaxis systems with degenerate diffusion. <i>Applied Mathematics Letters</i>, <i>161</i>, Article 109361. <a href=\"https://doi.org/10.1016/j.aml.2024.109361\">https://doi.org/10.1016/j.aml.2024.109361</a>","ieee":"T. Black, “Absence of dead-core formations in chemotaxis systems with degenerate diffusion,” <i>Applied Mathematics Letters</i>, vol. 161, Art. no. 109361, 2025, doi: <a href=\"https://doi.org/10.1016/j.aml.2024.109361\">10.1016/j.aml.2024.109361</a>.","ama":"Black T. Absence of dead-core formations in chemotaxis systems with degenerate diffusion. <i>Applied Mathematics Letters</i>. 2025;161. doi:<a href=\"https://doi.org/10.1016/j.aml.2024.109361\">10.1016/j.aml.2024.109361</a>","bibtex":"@article{Black_2025, title={Absence of dead-core formations in chemotaxis systems with degenerate diffusion}, volume={161}, DOI={<a href=\"https://doi.org/10.1016/j.aml.2024.109361\">10.1016/j.aml.2024.109361</a>}, number={109361}, journal={Applied Mathematics Letters}, publisher={Elsevier BV}, author={Black, Tobias}, year={2025} }","mla":"Black, Tobias. “Absence of Dead-Core Formations in Chemotaxis Systems with Degenerate Diffusion.” <i>Applied Mathematics Letters</i>, vol. 161, 109361, Elsevier BV, 2025, doi:<a href=\"https://doi.org/10.1016/j.aml.2024.109361\">10.1016/j.aml.2024.109361</a>."},"article_number":"109361","_id":"56960","publisher":"Elsevier BV","language":[{"iso":"eng"}],"doi":"10.1016/j.aml.2024.109361","user_id":"23686","volume":161,"status":"public","title":"Absence of dead-core formations in chemotaxis systems with degenerate diffusion","year":"2025","publication_identifier":{"issn":["0893-9659"]},"author":[{"id":"23686","orcid":"0000-0001-9963-0800","first_name":"Tobias","last_name":"Black","full_name":"Black, Tobias"}],"date_updated":"2024-11-08T13:30:02Z","publication_status":"published","intvolume":"       161"},{"article_number":"113555","language":[{"iso":"eng"}],"_id":"60205","publisher":"Elsevier BV","user_id":"23686","doi":"10.1016/j.jde.2025.113555","volume":443,"title":"Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system","status":"public","year":"2025","author":[{"id":"23686","full_name":"Black, Tobias","first_name":"Tobias","last_name":"Black","orcid":"0000-0001-9963-0800"}],"publication_identifier":{"issn":["0022-0396"]},"publication_status":"published","date_updated":"2025-06-13T11:13:22Z","intvolume":"       443","date_created":"2025-06-13T11:12:23Z","type":"journal_article","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"publication":"Journal of Differential Equations","citation":{"mla":"Black, Tobias. “Very Mild Diffusion Enhancement and Singular Sensitivity: Existence of Bounded Weak Solutions in a Two-Dimensional Chemotaxis-Navier–Stokes System.” <i>Journal of Differential Equations</i>, vol. 443, 113555, Elsevier BV, 2025, doi:<a href=\"https://doi.org/10.1016/j.jde.2025.113555\">10.1016/j.jde.2025.113555</a>.","ama":"Black T. Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system. <i>Journal of Differential Equations</i>. 2025;443. doi:<a href=\"https://doi.org/10.1016/j.jde.2025.113555\">10.1016/j.jde.2025.113555</a>","bibtex":"@article{Black_2025, title={Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system}, volume={443}, DOI={<a href=\"https://doi.org/10.1016/j.jde.2025.113555\">10.1016/j.jde.2025.113555</a>}, number={113555}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Black, Tobias}, year={2025} }","apa":"Black, T. (2025). Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system. <i>Journal of Differential Equations</i>, <i>443</i>, Article 113555. <a href=\"https://doi.org/10.1016/j.jde.2025.113555\">https://doi.org/10.1016/j.jde.2025.113555</a>","ieee":"T. Black, “Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system,” <i>Journal of Differential Equations</i>, vol. 443, Art. no. 113555, 2025, doi: <a href=\"https://doi.org/10.1016/j.jde.2025.113555\">10.1016/j.jde.2025.113555</a>.","chicago":"Black, Tobias. “Very Mild Diffusion Enhancement and Singular Sensitivity: Existence of Bounded Weak Solutions in a Two-Dimensional Chemotaxis-Navier–Stokes System.” <i>Journal of Differential Equations</i> 443 (2025). <a href=\"https://doi.org/10.1016/j.jde.2025.113555\">https://doi.org/10.1016/j.jde.2025.113555</a>.","short":"T. Black, Journal of Differential Equations 443 (2025)."}},{"date_updated":"2023-03-27T07:27:03Z","publication_status":"published","intvolume":"        73","year":"2023","title":"Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source","publication_identifier":{"issn":["1468-1218"]},"author":[{"id":"23686","orcid":"0000-0001-9963-0800","last_name":"Black","first_name":"Tobias","full_name":"Black, Tobias"},{"last_name":"Fuest","first_name":"Mario","full_name":"Fuest, Mario"},{"last_name":"Lankeit","first_name":"Johannes","full_name":"Lankeit, Johannes"},{"full_name":"Mizukami, Masaaki","last_name":"Mizukami","first_name":"Masaaki"}],"doi":"10.1016/j.nonrwa.2023.103868","article_number":"103868","language":[{"iso":"eng"}],"publication":"Nonlinear Analysis: Real World Applications","type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"date_created":"2023-03-27T07:25:58Z","status":"public","user_id":"23686","volume":73,"_id":"43105","publisher":"Elsevier BV","citation":{"apa":"Black, T., Fuest, M., Lankeit, J., &#38; Mizukami, M. (2023). Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source. <i>Nonlinear Analysis: Real World Applications</i>, <i>73</i>, Article 103868. <a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">https://doi.org/10.1016/j.nonrwa.2023.103868</a>","ieee":"T. Black, M. Fuest, J. Lankeit, and M. Mizukami, “Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source,” <i>Nonlinear Analysis: Real World Applications</i>, vol. 73, Art. no. 103868, 2023, doi: <a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>.","short":"T. Black, M. Fuest, J. Lankeit, M. Mizukami, Nonlinear Analysis: Real World Applications 73 (2023).","chicago":"Black, Tobias, Mario Fuest, Johannes Lankeit, and Masaaki Mizukami. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” <i>Nonlinear Analysis: Real World Applications</i> 73 (2023). <a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">https://doi.org/10.1016/j.nonrwa.2023.103868</a>.","mla":"Black, Tobias, et al. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” <i>Nonlinear Analysis: Real World Applications</i>, vol. 73, 103868, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>.","ama":"Black T, Fuest M, Lankeit J, Mizukami M. Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source. <i>Nonlinear Analysis: Real World Applications</i>. 2023;73. doi:<a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>","bibtex":"@article{Black_Fuest_Lankeit_Mizukami_2023, title={Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source}, volume={73}, DOI={<a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>}, number={103868}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV}, author={Black, Tobias and Fuest, Mario and Lankeit, Johannes and Mizukami, Masaaki}, year={2023} }"}},{"language":[{"iso":"eng"}],"article_number":"96","doi":"10.1007/s00526-022-02201-y","author":[{"first_name":"Tobias","orcid":"0000-0001-9963-0800","last_name":"Black","full_name":"Black, Tobias","id":"23686"},{"last_name":"Wu","first_name":"Chunyan","full_name":"Wu, Chunyan"}],"publication_identifier":{"issn":["0944-2669","1432-0835"]},"title":"Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation","year":"2022","intvolume":"        61","publication_status":"published","date_updated":"2023-07-10T11:37:27Z","date_created":"2022-12-21T09:50:59Z","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"type":"journal_article","keyword":["Applied Mathematics","Analysis"],"issue":"3","publication":"Calculus of Variations and Partial Differential Equations","_id":"34677","publisher":"Springer Science and Business Media LLC","volume":61,"user_id":"23686","status":"public","citation":{"ama":"Black T, Wu C. Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation. <i>Calculus of Variations and Partial Differential Equations</i>. 2022;61(3). doi:<a href=\"https://doi.org/10.1007/s00526-022-02201-y\">10.1007/s00526-022-02201-y</a>","bibtex":"@article{Black_Wu_2022, title={Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation}, volume={61}, DOI={<a href=\"https://doi.org/10.1007/s00526-022-02201-y\">10.1007/s00526-022-02201-y</a>}, number={396}, journal={Calculus of Variations and Partial Differential Equations}, publisher={Springer Science and Business Media LLC}, author={Black, Tobias and Wu, Chunyan}, year={2022} }","mla":"Black, Tobias, and Chunyan Wu. “Prescribed Signal Concentration on the Boundary: Eventual Smoothness in a Chemotaxis-Navier–Stokes System with Logistic Proliferation.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 61, no. 3, 96, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s00526-022-02201-y\">10.1007/s00526-022-02201-y</a>.","short":"T. Black, C. Wu, Calculus of Variations and Partial Differential Equations 61 (2022).","chicago":"Black, Tobias, and Chunyan Wu. “Prescribed Signal Concentration on the Boundary: Eventual Smoothness in a Chemotaxis-Navier–Stokes System with Logistic Proliferation.” <i>Calculus of Variations and Partial Differential Equations</i> 61, no. 3 (2022). <a href=\"https://doi.org/10.1007/s00526-022-02201-y\">https://doi.org/10.1007/s00526-022-02201-y</a>.","apa":"Black, T., &#38; Wu, C. (2022). Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation. <i>Calculus of Variations and Partial Differential Equations</i>, <i>61</i>(3), Article 96. <a href=\"https://doi.org/10.1007/s00526-022-02201-y\">https://doi.org/10.1007/s00526-022-02201-y</a>","ieee":"T. Black and C. Wu, “Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 61, no. 3, Art. no. 96, 2022, doi: <a href=\"https://doi.org/10.1007/s00526-022-02201-y\">10.1007/s00526-022-02201-y</a>."}},{"status":"public","volume":72,"user_id":"23686","publisher":"Springer Science and Business Media LLC","_id":"34673","citation":{"chicago":"Black, Tobias, Mario Fuest, and Johannes Lankeit. “Relaxed Parameter Conditions for Chemotactic Collapse in Logistic-Type Parabolic–Elliptic Keller–Segel Systems.” <i>Zeitschrift Für Angewandte Mathematik Und Physik</i> 72, no. 3 (2021). <a href=\"https://doi.org/10.1007/s00033-021-01524-8\">https://doi.org/10.1007/s00033-021-01524-8</a>.","short":"T. Black, M. Fuest, J. Lankeit, Zeitschrift Für Angewandte Mathematik Und Physik 72 (2021).","apa":"Black, T., Fuest, M., &#38; Lankeit, J. (2021). Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems. <i>Zeitschrift Für Angewandte Mathematik Und Physik</i>, <i>72</i>(3), Article 96. <a href=\"https://doi.org/10.1007/s00033-021-01524-8\">https://doi.org/10.1007/s00033-021-01524-8</a>","ieee":"T. Black, M. Fuest, and J. Lankeit, “Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems,” <i>Zeitschrift für angewandte Mathematik und Physik</i>, vol. 72, no. 3, Art. no. 96, 2021, doi: <a href=\"https://doi.org/10.1007/s00033-021-01524-8\">10.1007/s00033-021-01524-8</a>.","ama":"Black T, Fuest M, Lankeit J. Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems. <i>Zeitschrift für angewandte Mathematik und Physik</i>. 2021;72(3). doi:<a href=\"https://doi.org/10.1007/s00033-021-01524-8\">10.1007/s00033-021-01524-8</a>","bibtex":"@article{Black_Fuest_Lankeit_2021, title={Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems}, volume={72}, DOI={<a href=\"https://doi.org/10.1007/s00033-021-01524-8\">10.1007/s00033-021-01524-8</a>}, number={396}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer Science and Business Media LLC}, author={Black, Tobias and Fuest, Mario and Lankeit, Johannes}, year={2021} }","mla":"Black, Tobias, et al. “Relaxed Parameter Conditions for Chemotactic Collapse in Logistic-Type Parabolic–Elliptic Keller–Segel Systems.” <i>Zeitschrift Für Angewandte Mathematik Und Physik</i>, vol. 72, no. 3, 96, Springer Science and Business Media LLC, 2021, doi:<a href=\"https://doi.org/10.1007/s00033-021-01524-8\">10.1007/s00033-021-01524-8</a>."},"intvolume":"        72","publication_status":"published","date_updated":"2023-07-10T11:39:23Z","publication_identifier":{"issn":["0044-2275","1420-9039"]},"author":[{"first_name":"Tobias","last_name":"Black","orcid":"0000-0001-9963-0800","full_name":"Black, Tobias","id":"23686"},{"full_name":"Fuest, Mario","first_name":"Mario","last_name":"Fuest"},{"full_name":"Lankeit, Johannes","first_name":"Johannes","last_name":"Lankeit"}],"year":"2021","title":"Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems","doi":"10.1007/s00033-021-01524-8","language":[{"iso":"eng"}],"article_number":"96","issue":"3","publication":"Zeitschrift für angewandte Mathematik und Physik","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"keyword":["Applied Mathematics","General Physics and Astronomy","General Mathematics"],"type":"journal_article","date_created":"2022-12-21T09:48:36Z"},{"article_number":"135","language":[{"iso":"eng"}],"doi":"10.1007/s00033-021-01565-z","title":"Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation","year":"2021","author":[{"full_name":"Black, Tobias","first_name":"Tobias","last_name":"Black","orcid":"0000-0001-9963-0800","id":"23686"},{"last_name":"Wu","first_name":"Chunyan","full_name":"Wu, Chunyan"}],"publication_identifier":{"issn":["0044-2275","1420-9039"]},"publication_status":"published","date_updated":"2023-07-10T11:39:30Z","intvolume":"        72","date_created":"2022-12-21T09:48:45Z","keyword":["Applied Mathematics","General Physics and Astronomy","General Mathematics"],"type":"journal_article","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"publication":"Zeitschrift für angewandte Mathematik und Physik","issue":"4","_id":"34675","publisher":"Springer Science and Business Media LLC","user_id":"23686","volume":72,"status":"public","citation":{"mla":"Black, Tobias, and Chunyan Wu. “Prescribed Signal Concentration on the Boundary: Weak Solvability in a Chemotaxis-Stokes System with Proliferation.” <i>Zeitschrift Für Angewandte Mathematik Und Physik</i>, vol. 72, no. 4, 135, Springer Science and Business Media LLC, 2021, doi:<a href=\"https://doi.org/10.1007/s00033-021-01565-z\">10.1007/s00033-021-01565-z</a>.","bibtex":"@article{Black_Wu_2021, title={Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation}, volume={72}, DOI={<a href=\"https://doi.org/10.1007/s00033-021-01565-z\">10.1007/s00033-021-01565-z</a>}, number={4135}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer Science and Business Media LLC}, author={Black, Tobias and Wu, Chunyan}, year={2021} }","ama":"Black T, Wu C. Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation. <i>Zeitschrift für angewandte Mathematik und Physik</i>. 2021;72(4). doi:<a href=\"https://doi.org/10.1007/s00033-021-01565-z\">10.1007/s00033-021-01565-z</a>","ieee":"T. Black and C. Wu, “Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation,” <i>Zeitschrift für angewandte Mathematik und Physik</i>, vol. 72, no. 4, Art. no. 135, 2021, doi: <a href=\"https://doi.org/10.1007/s00033-021-01565-z\">10.1007/s00033-021-01565-z</a>.","apa":"Black, T., &#38; Wu, C. (2021). Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation. <i>Zeitschrift Für Angewandte Mathematik Und Physik</i>, <i>72</i>(4), Article 135. <a href=\"https://doi.org/10.1007/s00033-021-01565-z\">https://doi.org/10.1007/s00033-021-01565-z</a>","short":"T. Black, C. Wu, Zeitschrift Für Angewandte Mathematik Und Physik 72 (2021).","chicago":"Black, Tobias, and Chunyan Wu. “Prescribed Signal Concentration on the Boundary: Weak Solvability in a Chemotaxis-Stokes System with Proliferation.” <i>Zeitschrift Für Angewandte Mathematik Und Physik</i> 72, no. 4 (2021). <a href=\"https://doi.org/10.1007/s00033-021-01565-z\">https://doi.org/10.1007/s00033-021-01565-z</a>."}},{"status":"public","volume":32,"user_id":"31496","_id":"63291","publisher":"World Scientific Pub Co Pte Ltd","page":"137-173","citation":{"bibtex":"@article{Black_Winkler_2021, title={Global weak solutions and absorbing sets in a chemotaxis-Navier–Stokes system with prescribed signal concentration on the boundary}, volume={32}, DOI={<a href=\"https://doi.org/10.1142/s021820252250004x\">10.1142/s021820252250004x</a>}, number={01}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Black, Tobias and Winkler, Michael}, year={2021}, pages={137–173} }","ama":"Black T, Winkler M. Global weak solutions and absorbing sets in a chemotaxis-Navier–Stokes system with prescribed signal concentration on the boundary. <i>Mathematical Models and Methods in Applied Sciences</i>. 2021;32(01):137-173. doi:<a href=\"https://doi.org/10.1142/s021820252250004x\">10.1142/s021820252250004x</a>","mla":"Black, Tobias, and Michael Winkler. “Global Weak Solutions and Absorbing Sets in a Chemotaxis-Navier–Stokes System with Prescribed Signal Concentration on the Boundary.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 32, no. 01, World Scientific Pub Co Pte Ltd, 2021, pp. 137–73, doi:<a href=\"https://doi.org/10.1142/s021820252250004x\">10.1142/s021820252250004x</a>.","chicago":"Black, Tobias, and Michael Winkler. “Global Weak Solutions and Absorbing Sets in a Chemotaxis-Navier–Stokes System with Prescribed Signal Concentration on the Boundary.” <i>Mathematical Models and Methods in Applied Sciences</i> 32, no. 01 (2021): 137–73. <a href=\"https://doi.org/10.1142/s021820252250004x\">https://doi.org/10.1142/s021820252250004x</a>.","short":"T. Black, M. Winkler, Mathematical Models and Methods in Applied Sciences 32 (2021) 137–173.","ieee":"T. Black and M. Winkler, “Global weak solutions and absorbing sets in a chemotaxis-Navier–Stokes system with prescribed signal concentration on the boundary,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 32, no. 01, pp. 137–173, 2021, doi: <a href=\"https://doi.org/10.1142/s021820252250004x\">10.1142/s021820252250004x</a>.","apa":"Black, T., &#38; Winkler, M. (2021). Global weak solutions and absorbing sets in a chemotaxis-Navier–Stokes system with prescribed signal concentration on the boundary. <i>Mathematical Models and Methods in Applied Sciences</i>, <i>32</i>(01), 137–173. <a href=\"https://doi.org/10.1142/s021820252250004x\">https://doi.org/10.1142/s021820252250004x</a>"},"intvolume":"        32","publication_status":"published","date_updated":"2025-12-18T20:08:01Z","publication_identifier":{"issn":["0218-2025","1793-6314"]},"author":[{"orcid":"0000-0001-9963-0800","last_name":"Black","first_name":"Tobias","full_name":"Black, Tobias","id":"23686"},{"id":"31496","first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"year":"2021","title":"Global weak solutions and absorbing sets in a chemotaxis-Navier–Stokes system with prescribed signal concentration on the boundary","doi":"10.1142/s021820252250004x","language":[{"iso":"eng"}],"abstract":[{"text":"<jats:p> An initial-boundary value problem for a coupled chemotaxis-Navier–Stokes model with porous medium type diffusion is considered. Previous related literature has provided profound knowledge in cases when the system is augmented with no-flux/no-flux/no-slip boundary conditions for the density of cells, the chemical concentration and the fluid velocity field, respectively; in particular, available qualitative results strongly indicate that only trivial solution behavior can be expected on large time scales. In line with refined modeling approaches to oxygen evolution near fluid-air interfaces, this study now focuses on situations involving a fixed chemoattractant concentration on the boundary. Despite an apparent loss of mathematically favorable energy structures thereby induced, by means of an alternative variational approach a basic theory of global existence is developed in a natural framework of weak solvability. Beyond this, some additional qualitative information on the large time behavior of these solutions is derived by identifying a certain global relaxation property. Specifically, a second result asserts, within a suitable topological setting, the existence of a bounded set which eventually absorbs each individual of the obtained trajectories, and the diameter of which is bounded only by the physically relevant quantities of total population size and prescribed boundary concentration of the chemical signal. </jats:p>","lang":"eng"}],"publication":"Mathematical Models and Methods in Applied Sciences","issue":"01","type":"journal_article","date_created":"2025-12-18T19:20:48Z"},{"user_id":"23686","volume":30,"page":"1075-1117","publisher":"World Scientific Pub Co Pte Lt","_id":"34670","status":"public","citation":{"mla":"Black, Tobias. “Global Generalized Solutions to a Forager–Exploiter Model with Superlinear Degradation and Their Eventual Regularity Properties.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 30, no. 06, World Scientific Pub Co Pte Lt, 2020, pp. 1075–117, doi:<a href=\"https://doi.org/10.1142/s0218202520400072\">10.1142/s0218202520400072</a>.","bibtex":"@article{Black_2020, title={Global generalized solutions to a forager–exploiter model with superlinear degradation and their eventual regularity properties}, volume={30}, DOI={<a href=\"https://doi.org/10.1142/s0218202520400072\">10.1142/s0218202520400072</a>}, number={06}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World Scientific Pub Co Pte Lt}, author={Black, Tobias}, year={2020}, pages={1075–1117} }","ama":"Black T. Global generalized solutions to a forager–exploiter model with superlinear degradation and their eventual regularity properties. <i>Mathematical Models and Methods in Applied Sciences</i>. 2020;30(06):1075-1117. doi:<a href=\"https://doi.org/10.1142/s0218202520400072\">10.1142/s0218202520400072</a>","ieee":"T. Black, “Global generalized solutions to a forager–exploiter model with superlinear degradation and their eventual regularity properties,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 30, no. 06, pp. 1075–1117, 2020, doi: <a href=\"https://doi.org/10.1142/s0218202520400072\">10.1142/s0218202520400072</a>.","apa":"Black, T. (2020). Global generalized solutions to a forager–exploiter model with superlinear degradation and their eventual regularity properties. <i>Mathematical Models and Methods in Applied Sciences</i>, <i>30</i>(06), 1075–1117. <a href=\"https://doi.org/10.1142/s0218202520400072\">https://doi.org/10.1142/s0218202520400072</a>","short":"T. Black, Mathematical Models and Methods in Applied Sciences 30 (2020) 1075–1117.","chicago":"Black, Tobias. “Global Generalized Solutions to a Forager–Exploiter Model with Superlinear Degradation and Their Eventual Regularity Properties.” <i>Mathematical Models and Methods in Applied Sciences</i> 30, no. 06 (2020): 1075–1117. <a href=\"https://doi.org/10.1142/s0218202520400072\">https://doi.org/10.1142/s0218202520400072</a>."},"doi":"10.1142/s0218202520400072","language":[{"iso":"eng"}],"date_updated":"2023-07-10T11:39:59Z","publication_status":"published","intvolume":"        30","title":"Global generalized solutions to a forager–exploiter model with superlinear degradation and their eventual regularity properties","year":"2020","author":[{"id":"23686","full_name":"Black, Tobias","orcid":"0000-0001-9963-0800","first_name":"Tobias","last_name":"Black"}],"publication_identifier":{"issn":["0218-2025","1793-6314"]},"type":"journal_article","keyword":["Applied Mathematics","Modeling and Simulation"],"department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"date_created":"2022-12-21T09:48:11Z","issue":"06","publication":"Mathematical Models and Methods in Applied Sciences"},{"citation":{"short":"T. Black, Discrete &#38;amp; Continuous Dynamical Systems - S 13 (2019) 119–137.","chicago":"Black, Tobias. “Global Generalized Solutions to a Parabolic-Elliptic Keller-Segel System with Singular Sensitivity.” <i>Discrete &#38;amp; Continuous Dynamical Systems - S</i> 13, no. 2 (2019): 119–37. <a href=\"https://doi.org/10.3934/dcdss.2020007\">https://doi.org/10.3934/dcdss.2020007</a>.","ieee":"T. Black, “Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity,” <i>Discrete &#38;amp; Continuous Dynamical Systems - S</i>, vol. 13, no. 2, pp. 119–137, 2019, doi: <a href=\"https://doi.org/10.3934/dcdss.2020007\">10.3934/dcdss.2020007</a>.","apa":"Black, T. (2019). Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity. <i>Discrete &#38;amp; Continuous Dynamical Systems - S</i>, <i>13</i>(2), 119–137. <a href=\"https://doi.org/10.3934/dcdss.2020007\">https://doi.org/10.3934/dcdss.2020007</a>","bibtex":"@article{Black_2019, title={Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity}, volume={13}, DOI={<a href=\"https://doi.org/10.3934/dcdss.2020007\">10.3934/dcdss.2020007</a>}, number={2}, journal={Discrete &#38;amp; Continuous Dynamical Systems - S}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Black, Tobias}, year={2019}, pages={119–137} }","ama":"Black T. Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity. <i>Discrete &#38;amp; Continuous Dynamical Systems - S</i>. 2019;13(2):119-137. doi:<a href=\"https://doi.org/10.3934/dcdss.2020007\">10.3934/dcdss.2020007</a>","mla":"Black, Tobias. “Global Generalized Solutions to a Parabolic-Elliptic Keller-Segel System with Singular Sensitivity.” <i>Discrete &#38;amp; Continuous Dynamical Systems - S</i>, vol. 13, no. 2, American Institute of Mathematical Sciences (AIMS), 2019, pp. 119–37, doi:<a href=\"https://doi.org/10.3934/dcdss.2020007\">10.3934/dcdss.2020007</a>."},"status":"public","page":"119-137","_id":"34672","publisher":"American Institute of Mathematical Sciences (AIMS)","user_id":"23686","volume":13,"issue":"2","publication":"Discrete &amp; Continuous Dynamical Systems - S","date_created":"2022-12-21T09:48:28Z","type":"journal_article","keyword":["Applied Mathematics","Discrete Mathematics and Combinatorics","Analysis"],"department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"title":"Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity","year":"2019","publication_identifier":{"issn":["1937-1179"]},"author":[{"id":"23686","full_name":"Black, Tobias","last_name":"Black","orcid":"0000-0001-9963-0800","first_name":"Tobias"}],"date_updated":"2022-12-21T10:04:44Z","publication_status":"published","intvolume":"        13","language":[{"iso":"eng"}],"doi":"10.3934/dcdss.2020007"},{"volume":22,"user_id":"23686","_id":"34669","publisher":"Springer Science and Business Media LLC","status":"public","citation":{"bibtex":"@article{Black_2019, title={The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System}, volume={22}, DOI={<a href=\"https://doi.org/10.1007/s00021-019-0464-z\">10.1007/s00021-019-0464-z</a>}, number={11}, journal={Journal of Mathematical Fluid Mechanics}, publisher={Springer Science and Business Media LLC}, author={Black, Tobias}, year={2019} }","short":"T. Black, Journal of Mathematical Fluid Mechanics 22 (2019).","ama":"Black T. The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System. <i>Journal of Mathematical Fluid Mechanics</i>. 2019;22(1). doi:<a href=\"https://doi.org/10.1007/s00021-019-0464-z\">10.1007/s00021-019-0464-z</a>","chicago":"Black, Tobias. “The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System.” <i>Journal of Mathematical Fluid Mechanics</i> 22, no. 1 (2019). <a href=\"https://doi.org/10.1007/s00021-019-0464-z\">https://doi.org/10.1007/s00021-019-0464-z</a>.","ieee":"T. Black, “The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System,” <i>Journal of Mathematical Fluid Mechanics</i>, vol. 22, no. 1, Art. no. 1, 2019, doi: <a href=\"https://doi.org/10.1007/s00021-019-0464-z\">10.1007/s00021-019-0464-z</a>.","apa":"Black, T. (2019). The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System. <i>Journal of Mathematical Fluid Mechanics</i>, <i>22</i>(1), Article 1. <a href=\"https://doi.org/10.1007/s00021-019-0464-z\">https://doi.org/10.1007/s00021-019-0464-z</a>","mla":"Black, Tobias. “The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System.” <i>Journal of Mathematical Fluid Mechanics</i>, vol. 22, no. 1, 1, Springer Science and Business Media LLC, 2019, doi:<a href=\"https://doi.org/10.1007/s00021-019-0464-z\">10.1007/s00021-019-0464-z</a>."},"doi":"10.1007/s00021-019-0464-z","language":[{"iso":"eng"}],"article_number":"1","intvolume":"        22","publication_status":"published","date_updated":"2022-12-21T10:04:29Z","publication_identifier":{"issn":["1422-6928","1422-6952"]},"author":[{"full_name":"Black, Tobias","orcid":"0000-0001-9963-0800","first_name":"Tobias","last_name":"Black","id":"23686"}],"title":"The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System","year":"2019","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"keyword":["Applied Mathematics","Computational Mathematics","Condensed Matter Physics","Mathematical Physics"],"type":"journal_article","date_created":"2022-12-21T09:47:56Z","publication":"Journal of Mathematical Fluid Mechanics","issue":"1"},{"issue":"9","publication":"Mathematical Methods in the Applied Sciences","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"type":"journal_article","keyword":["General Engineering","General Mathematics"],"date_created":"2022-12-21T09:47:47Z","intvolume":"        42","date_updated":"2022-12-21T10:04:36Z","publication_status":"published","publication_identifier":{"issn":["0170-4214","1099-1476"]},"author":[{"full_name":"Black, Tobias","orcid":"0000-0001-9963-0800","last_name":"Black","first_name":"Tobias","id":"23686"},{"last_name":"Lankeit","first_name":"Johannes","full_name":"Lankeit, Johannes"},{"full_name":"Mizukami, Masaaki","first_name":"Masaaki","last_name":"Mizukami"}],"year":"2019","title":"A Keller‐Segel‐fluid system with singular sensitivity: Generalized solutions","doi":"10.1002/mma.5561","language":[{"iso":"eng"}],"citation":{"ieee":"T. Black, J. Lankeit, and M. Mizukami, “A Keller‐Segel‐fluid system with singular sensitivity: Generalized solutions,” <i>Mathematical Methods in the Applied Sciences</i>, vol. 42, no. 9, pp. 3002–3020, 2019, doi: <a href=\"https://doi.org/10.1002/mma.5561\">10.1002/mma.5561</a>.","apa":"Black, T., Lankeit, J., &#38; Mizukami, M. (2019). A Keller‐Segel‐fluid system with singular sensitivity: Generalized solutions. <i>Mathematical Methods in the Applied Sciences</i>, <i>42</i>(9), 3002–3020. <a href=\"https://doi.org/10.1002/mma.5561\">https://doi.org/10.1002/mma.5561</a>","mla":"Black, Tobias, et al. “A Keller‐Segel‐fluid System with Singular Sensitivity: Generalized Solutions.” <i>Mathematical Methods in the Applied Sciences</i>, vol. 42, no. 9, Wiley, 2019, pp. 3002–20, doi:<a href=\"https://doi.org/10.1002/mma.5561\">10.1002/mma.5561</a>.","bibtex":"@article{Black_Lankeit_Mizukami_2019, title={A Keller‐Segel‐fluid system with singular sensitivity: Generalized solutions}, volume={42}, DOI={<a href=\"https://doi.org/10.1002/mma.5561\">10.1002/mma.5561</a>}, number={9}, journal={Mathematical Methods in the Applied Sciences}, publisher={Wiley}, author={Black, Tobias and Lankeit, Johannes and Mizukami, Masaaki}, year={2019}, pages={3002–3020} }","chicago":"Black, Tobias, Johannes Lankeit, and Masaaki Mizukami. “A Keller‐Segel‐fluid System with Singular Sensitivity: Generalized Solutions.” <i>Mathematical Methods in the Applied Sciences</i> 42, no. 9 (2019): 3002–20. <a href=\"https://doi.org/10.1002/mma.5561\">https://doi.org/10.1002/mma.5561</a>.","ama":"Black T, Lankeit J, Mizukami M. A Keller‐Segel‐fluid system with singular sensitivity: Generalized solutions. <i>Mathematical Methods in the Applied Sciences</i>. 2019;42(9):3002-3020. doi:<a href=\"https://doi.org/10.1002/mma.5561\">10.1002/mma.5561</a>","short":"T. Black, J. Lankeit, M. Mizukami, Mathematical Methods in the Applied Sciences 42 (2019) 3002–3020."},"status":"public","volume":42,"user_id":"23686","_id":"34668","publisher":"Wiley","page":"3002-3020"},{"status":"public","publisher":"Informa UK Limited","_id":"34671","page":"2877-2891","volume":99,"user_id":"23686","citation":{"apa":"Black, T., Lankeit, J., &#38; Mizukami, M. (2019). Stabilization in the Keller–Segel system with signal-dependent sensitivity. <i>Applicable Analysis</i>, <i>99</i>(16), 2877–2891. <a href=\"https://doi.org/10.1080/00036811.2019.1585534\">https://doi.org/10.1080/00036811.2019.1585534</a>","mla":"Black, Tobias, et al. “Stabilization in the Keller–Segel System with Signal-Dependent Sensitivity.” <i>Applicable Analysis</i>, vol. 99, no. 16, Informa UK Limited, 2019, pp. 2877–91, doi:<a href=\"https://doi.org/10.1080/00036811.2019.1585534\">10.1080/00036811.2019.1585534</a>.","ieee":"T. Black, J. Lankeit, and M. Mizukami, “Stabilization in the Keller–Segel system with signal-dependent sensitivity,” <i>Applicable Analysis</i>, vol. 99, no. 16, pp. 2877–2891, 2019, doi: <a href=\"https://doi.org/10.1080/00036811.2019.1585534\">10.1080/00036811.2019.1585534</a>.","chicago":"Black, Tobias, Johannes Lankeit, and Masaaki Mizukami. “Stabilization in the Keller–Segel System with Signal-Dependent Sensitivity.” <i>Applicable Analysis</i> 99, no. 16 (2019): 2877–91. <a href=\"https://doi.org/10.1080/00036811.2019.1585534\">https://doi.org/10.1080/00036811.2019.1585534</a>.","ama":"Black T, Lankeit J, Mizukami M. Stabilization in the Keller–Segel system with signal-dependent sensitivity. <i>Applicable Analysis</i>. 2019;99(16):2877-2891. doi:<a href=\"https://doi.org/10.1080/00036811.2019.1585534\">10.1080/00036811.2019.1585534</a>","short":"T. Black, J. Lankeit, M. Mizukami, Applicable Analysis 99 (2019) 2877–2891.","bibtex":"@article{Black_Lankeit_Mizukami_2019, title={Stabilization in the Keller–Segel system with signal-dependent sensitivity}, volume={99}, DOI={<a href=\"https://doi.org/10.1080/00036811.2019.1585534\">10.1080/00036811.2019.1585534</a>}, number={16}, journal={Applicable Analysis}, publisher={Informa UK Limited}, author={Black, Tobias and Lankeit, Johannes and Mizukami, Masaaki}, year={2019}, pages={2877–2891} }"},"author":[{"id":"23686","full_name":"Black, Tobias","first_name":"Tobias","orcid":"0000-0001-9963-0800","last_name":"Black"},{"last_name":"Lankeit","first_name":"Johannes","full_name":"Lankeit, Johannes"},{"full_name":"Mizukami, Masaaki","last_name":"Mizukami","first_name":"Masaaki"}],"publication_identifier":{"issn":["0003-6811","1563-504X"]},"year":"2019","title":"Stabilization in the Keller–Segel system with signal-dependent sensitivity","intvolume":"        99","publication_status":"published","date_updated":"2022-12-21T10:04:50Z","language":[{"iso":"eng"}],"doi":"10.1080/00036811.2019.1585534","publication":"Applicable Analysis","issue":"16","date_created":"2022-12-21T09:48:19Z","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"type":"journal_article","keyword":["Applied Mathematics","Analysis"]},{"issue":"4","publication":"SIAM Journal on Mathematical Analysis","date_created":"2022-12-21T09:47:01Z","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"author":[{"full_name":"Black, Tobias","orcid":"0000-0001-9963-0800","last_name":"Black","first_name":"Tobias","id":"23686"}],"publication_identifier":{"issn":["0036-1410","1095-7154"]},"title":"Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion","year":"2018","intvolume":"        50","date_updated":"2022-12-21T10:04:57Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.1137/17m1159488","citation":{"mla":"Black, Tobias. “Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 50, no. 4, Society for Industrial &#38; Applied Mathematics (SIAM), 2018, pp. 4087–116, doi:<a href=\"https://doi.org/10.1137/17m1159488\">10.1137/17m1159488</a>.","bibtex":"@article{Black_2018, title={Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion}, volume={50}, DOI={<a href=\"https://doi.org/10.1137/17m1159488\">10.1137/17m1159488</a>}, number={4}, journal={SIAM Journal on Mathematical Analysis}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={Black, Tobias}, year={2018}, pages={4087–4116} }","ama":"Black T. Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion. <i>SIAM Journal on Mathematical Analysis</i>. 2018;50(4):4087-4116. doi:<a href=\"https://doi.org/10.1137/17m1159488\">10.1137/17m1159488</a>","ieee":"T. Black, “Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 50, no. 4, pp. 4087–4116, 2018, doi: <a href=\"https://doi.org/10.1137/17m1159488\">10.1137/17m1159488</a>.","apa":"Black, T. (2018). Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion. <i>SIAM Journal on Mathematical Analysis</i>, <i>50</i>(4), 4087–4116. <a href=\"https://doi.org/10.1137/17m1159488\">https://doi.org/10.1137/17m1159488</a>","chicago":"Black, Tobias. “Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion.” <i>SIAM Journal on Mathematical Analysis</i> 50, no. 4 (2018): 4087–4116. <a href=\"https://doi.org/10.1137/17m1159488\">https://doi.org/10.1137/17m1159488</a>.","short":"T. Black, SIAM Journal on Mathematical Analysis 50 (2018) 4087–4116."},"status":"public","_id":"34664","publisher":"Society for Industrial & Applied Mathematics (SIAM)","page":"4087-4116","volume":50,"user_id":"23686"},{"citation":{"ama":"Black T. Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D. <i>Journal of Differential Equations</i>. 2018;265(5):2296-2339. doi:<a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">10.1016/j.jde.2018.04.035</a>","bibtex":"@article{Black_2018, title={Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D}, volume={265}, DOI={<a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">10.1016/j.jde.2018.04.035</a>}, number={5}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Black, Tobias}, year={2018}, pages={2296–2339} }","mla":"Black, Tobias. “Eventual Smoothness of Generalized Solutions to a Singular Chemotaxis-Stokes System in 2D.” <i>Journal of Differential Equations</i>, vol. 265, no. 5, Elsevier BV, 2018, pp. 2296–339, doi:<a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">10.1016/j.jde.2018.04.035</a>.","chicago":"Black, Tobias. “Eventual Smoothness of Generalized Solutions to a Singular Chemotaxis-Stokes System in 2D.” <i>Journal of Differential Equations</i> 265, no. 5 (2018): 2296–2339. <a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">https://doi.org/10.1016/j.jde.2018.04.035</a>.","short":"T. Black, Journal of Differential Equations 265 (2018) 2296–2339.","apa":"Black, T. (2018). Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D. <i>Journal of Differential Equations</i>, <i>265</i>(5), 2296–2339. <a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">https://doi.org/10.1016/j.jde.2018.04.035</a>","ieee":"T. Black, “Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D,” <i>Journal of Differential Equations</i>, vol. 265, no. 5, pp. 2296–2339, 2018, doi: <a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">10.1016/j.jde.2018.04.035</a>."},"status":"public","user_id":"23686","volume":265,"page":"2296-2339","_id":"34666","publisher":"Elsevier BV","issue":"5","publication":"Journal of Differential Equations","keyword":["Analysis","Applied Mathematics"],"type":"journal_article","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"date_created":"2022-12-21T09:47:19Z","publication_status":"published","date_updated":"2022-12-21T10:05:11Z","intvolume":"       265","year":"2018","title":"Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D","publication_identifier":{"issn":["0022-0396"]},"author":[{"full_name":"Black, Tobias","orcid":"0000-0001-9963-0800","first_name":"Tobias","last_name":"Black","id":"23686"}],"doi":"10.1016/j.jde.2018.04.035","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"doi":"10.1016/j.na.2018.10.003","publication_identifier":{"issn":["0362-546X"]},"author":[{"id":"23686","full_name":"Black, Tobias","orcid":"0000-0001-9963-0800","first_name":"Tobias","last_name":"Black"}],"year":"2018","title":"Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions","intvolume":"       180","publication_status":"published","date_updated":"2022-12-21T10:05:04Z","date_created":"2022-12-21T09:47:30Z","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"type":"journal_article","keyword":["Applied Mathematics","Analysis"],"publication":"Nonlinear Analysis","_id":"34667","publisher":"Elsevier BV","page":"129-153","volume":180,"user_id":"23686","status":"public","citation":{"short":"T. Black, Nonlinear Analysis 180 (2018) 129–153.","chicago":"Black, Tobias. “Global Solvability of Chemotaxis–Fluid Systems with Nonlinear Diffusion and Matrix-Valued Sensitivities in Three Dimensions.” <i>Nonlinear Analysis</i> 180 (2018): 129–53. <a href=\"https://doi.org/10.1016/j.na.2018.10.003\">https://doi.org/10.1016/j.na.2018.10.003</a>.","ieee":"T. Black, “Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions,” <i>Nonlinear Analysis</i>, vol. 180, pp. 129–153, 2018, doi: <a href=\"https://doi.org/10.1016/j.na.2018.10.003\">10.1016/j.na.2018.10.003</a>.","apa":"Black, T. (2018). Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions. <i>Nonlinear Analysis</i>, <i>180</i>, 129–153. <a href=\"https://doi.org/10.1016/j.na.2018.10.003\">https://doi.org/10.1016/j.na.2018.10.003</a>","bibtex":"@article{Black_2018, title={Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions}, volume={180}, DOI={<a href=\"https://doi.org/10.1016/j.na.2018.10.003\">10.1016/j.na.2018.10.003</a>}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Black, Tobias}, year={2018}, pages={129–153} }","ama":"Black T. Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions. <i>Nonlinear Analysis</i>. 2018;180:129-153. doi:<a href=\"https://doi.org/10.1016/j.na.2018.10.003\">10.1016/j.na.2018.10.003</a>","mla":"Black, Tobias. “Global Solvability of Chemotaxis–Fluid Systems with Nonlinear Diffusion and Matrix-Valued Sensitivities in Three Dimensions.” <i>Nonlinear Analysis</i>, vol. 180, Elsevier BV, 2018, pp. 129–53, doi:<a href=\"https://doi.org/10.1016/j.na.2018.10.003\">10.1016/j.na.2018.10.003</a>."}},{"doi":"10.3934/dcdsb.2017061","language":[{"iso":"eng"}],"intvolume":"        22","publication_status":"published","date_updated":"2022-12-21T10:05:19Z","publication_identifier":{"issn":["1553-524X"]},"author":[{"full_name":"Black, Tobias","first_name":"Tobias","last_name":"Black","orcid":"0000-0001-9963-0800","id":"23686"}],"title":"Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals","year":"2017","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"keyword":["Applied Mathematics","Discrete Mathematics and Combinatorics"],"type":"journal_article","date_created":"2022-12-21T09:46:50Z","issue":"4","publication":"Discrete &amp; Continuous Dynamical Systems - B","volume":22,"user_id":"23686","publisher":"American Institute of Mathematical Sciences (AIMS)","_id":"34663","page":"1253-1272","status":"public","citation":{"ama":"Black T. Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals. <i>Discrete &#38;amp; Continuous Dynamical Systems - B</i>. 2017;22(4):1253-1272. doi:<a href=\"https://doi.org/10.3934/dcdsb.2017061\">10.3934/dcdsb.2017061</a>","bibtex":"@article{Black_2017, title={Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals}, volume={22}, DOI={<a href=\"https://doi.org/10.3934/dcdsb.2017061\">10.3934/dcdsb.2017061</a>}, number={4}, journal={Discrete &#38;amp; Continuous Dynamical Systems - B}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Black, Tobias}, year={2017}, pages={1253–1272} }","mla":"Black, Tobias. “Global Existence and Asymptotic Stability in a Competitive Two-Species Chemotaxis System with Two Signals.” <i>Discrete &#38;amp; Continuous Dynamical Systems - B</i>, vol. 22, no. 4, American Institute of Mathematical Sciences (AIMS), 2017, pp. 1253–72, doi:<a href=\"https://doi.org/10.3934/dcdsb.2017061\">10.3934/dcdsb.2017061</a>.","short":"T. Black, Discrete &#38;amp; Continuous Dynamical Systems - B 22 (2017) 1253–1272.","chicago":"Black, Tobias. “Global Existence and Asymptotic Stability in a Competitive Two-Species Chemotaxis System with Two Signals.” <i>Discrete &#38;amp; Continuous Dynamical Systems - B</i> 22, no. 4 (2017): 1253–72. <a href=\"https://doi.org/10.3934/dcdsb.2017061\">https://doi.org/10.3934/dcdsb.2017061</a>.","apa":"Black, T. (2017). Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals. <i>Discrete &#38;amp; Continuous Dynamical Systems - B</i>, <i>22</i>(4), 1253–1272. <a href=\"https://doi.org/10.3934/dcdsb.2017061\">https://doi.org/10.3934/dcdsb.2017061</a>","ieee":"T. Black, “Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals,” <i>Discrete &#38;amp; Continuous Dynamical Systems - B</i>, vol. 22, no. 4, pp. 1253–1272, 2017, doi: <a href=\"https://doi.org/10.3934/dcdsb.2017061\">10.3934/dcdsb.2017061</a>."}},{"citation":{"ieee":"T. Black, J. Lankeit, and M. Mizukami, “Singular sensitivity in a Keller–Segel-fluid system,” <i>Journal of Evolution Equations</i>, vol. 18, no. 2, pp. 561–581, 2017, doi: <a href=\"https://doi.org/10.1007/s00028-017-0411-5\">10.1007/s00028-017-0411-5</a>.","apa":"Black, T., Lankeit, J., &#38; Mizukami, M. (2017). Singular sensitivity in a Keller–Segel-fluid system. <i>Journal of Evolution Equations</i>, <i>18</i>(2), 561–581. <a href=\"https://doi.org/10.1007/s00028-017-0411-5\">https://doi.org/10.1007/s00028-017-0411-5</a>","chicago":"Black, Tobias, Johannes Lankeit, and Masaaki Mizukami. “Singular Sensitivity in a Keller–Segel-Fluid System.” <i>Journal of Evolution Equations</i> 18, no. 2 (2017): 561–81. <a href=\"https://doi.org/10.1007/s00028-017-0411-5\">https://doi.org/10.1007/s00028-017-0411-5</a>.","short":"T. Black, J. Lankeit, M. Mizukami, Journal of Evolution Equations 18 (2017) 561–581.","mla":"Black, Tobias, et al. “Singular Sensitivity in a Keller–Segel-Fluid System.” <i>Journal of Evolution Equations</i>, vol. 18, no. 2, Springer Science and Business Media LLC, 2017, pp. 561–81, doi:<a href=\"https://doi.org/10.1007/s00028-017-0411-5\">10.1007/s00028-017-0411-5</a>.","bibtex":"@article{Black_Lankeit_Mizukami_2017, title={Singular sensitivity in a Keller–Segel-fluid system}, volume={18}, DOI={<a href=\"https://doi.org/10.1007/s00028-017-0411-5\">10.1007/s00028-017-0411-5</a>}, number={2}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Black, Tobias and Lankeit, Johannes and Mizukami, Masaaki}, year={2017}, pages={561–581} }","ama":"Black T, Lankeit J, Mizukami M. Singular sensitivity in a Keller–Segel-fluid system. <i>Journal of Evolution Equations</i>. 2017;18(2):561-581. doi:<a href=\"https://doi.org/10.1007/s00028-017-0411-5\">10.1007/s00028-017-0411-5</a>"},"status":"public","volume":18,"user_id":"23686","_id":"34665","publisher":"Springer Science and Business Media LLC","page":"561-581","issue":"2","publication":"Journal of Evolution Equations","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"type":"journal_article","keyword":["Mathematics (miscellaneous)"],"date_created":"2022-12-21T09:47:13Z","intvolume":"        18","date_updated":"2022-12-21T10:05:25Z","publication_status":"published","publication_identifier":{"issn":["1424-3199","1424-3202"]},"author":[{"first_name":"Tobias","orcid":"0000-0001-9963-0800","last_name":"Black","full_name":"Black, Tobias","id":"23686"},{"full_name":"Lankeit, Johannes","first_name":"Johannes","last_name":"Lankeit"},{"full_name":"Mizukami, Masaaki","first_name":"Masaaki","last_name":"Mizukami"}],"year":"2017","title":"Singular sensitivity in a Keller–Segel-fluid system","doi":"10.1007/s00028-017-0411-5","language":[{"iso":"eng"}]}]