[{"status":"public","abstract":[{"text":"<p style='text-indent:20px;'>The chemotaxis system</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE1\"> \\begin{document}$ \\begin{array}{l}\\left\\{ \\begin{array}{l} \tu_t = \\nabla \\cdot \\big( D(u) \\nabla u \\big) - \\nabla \\cdot \\big( uS(x, u, v)\\cdot \\nabla v\\big), \\\\ \tv_t = \\Delta v -uv, \\end{array} \\right. \\end{array} $\\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>is considered in a bounded domain <inline-formula><tex-math id=\"M1\">\\begin{document}$ \\Omega\\subset \\mathbb{R}^n $\\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M2\">\\begin{document}$ n\\ge 2 $\\end{document}</tex-math></inline-formula>, with smooth boundary.</p><p style='text-indent:20px;'>It is shown that if <inline-formula><tex-math id=\"M3\">\\begin{document}$ D: [0, \\infty) \\to [0, \\infty) $\\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M4\">\\begin{document}$ S: \\overline{\\Omega}\\times [0, \\infty)\\times (0, \\infty)\\to \\mathbb{R}^{n\\times n} $\\end{document}</tex-math></inline-formula> are suitably smooth functions satisfying</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE2\"> \\begin{document}$ \\begin{array}{l}D(u) \\ge k_D u^{m-1} \t\\qquad {\\rm{for\\; all}}\\; u\\ge 0 \\end{array} $\\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>and</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE3\"> \\begin{document}$ \\begin{array}{l}|S(x, u, v)| \\le \\frac{S_0(v)}{v^\\alpha} \\qquad {\\rm{for\\; all}}\\; (x, u, v)\\; \\in \\Omega\\times (0, \\infty)^2 \\end{array} $\\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>with some</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE4\"> \\begin{document}$ \\begin{array}{l}m>\\frac{3n-2}{2n} \t\\qquad {\\rm{and}}\\;\\alpha\\in [0, 1), \\end{array} $\\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>and with some <inline-formula><tex-math id=\"M5\">\\begin{document}$ k_D>0 $\\end{document}</tex-math></inline-formula> and nondecreasing <inline-formula><tex-math id=\"M6\">\\begin{document}$ S_0: (0, \\infty)\\to (0, \\infty) $\\end{document}</tex-math></inline-formula>, then for all suitably regular initial data a corresponding no-flux type initial-boundary value problem admits a global bounded weak solution which actually is smooth and classical if <inline-formula><tex-math id=\"M7\">\\begin{document}$ D(0)>0 $\\end{document}</tex-math></inline-formula>.</p>","lang":"eng"}],"publication":"Discrete and Continuous Dynamical Systems - B","type":"journal_article","language":[{"iso":"eng"}],"article_number":"6565","user_id":"31496","_id":"63312","intvolume":" 27","citation":{"apa":"Winkler, M. (2022). Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities. Discrete and Continuous Dynamical Systems - B, 27(11), Article 6565. https://doi.org/10.3934/dcdsb.2022009","mla":"Winkler, Michael. “Approaching Logarithmic Singularities in Quasilinear Chemotaxis-Consumption Systems with Signal-Dependent Sensitivities.” Discrete and Continuous Dynamical Systems - B, vol. 27, no. 11, 6565, American Institute of Mathematical Sciences (AIMS), 2022, doi:10.3934/dcdsb.2022009.","short":"M. Winkler, Discrete and Continuous Dynamical Systems - B 27 (2022).","bibtex":"@article{Winkler_2022, title={Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities}, volume={27}, DOI={10.3934/dcdsb.2022009}, number={116565}, journal={Discrete and Continuous Dynamical Systems - B}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Winkler, Michael}, year={2022} }","ama":"Winkler M. Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities. Discrete and Continuous Dynamical Systems - B. 2022;27(11). doi:10.3934/dcdsb.2022009","chicago":"Winkler, Michael. “Approaching Logarithmic Singularities in Quasilinear Chemotaxis-Consumption Systems with Signal-Dependent Sensitivities.” Discrete and Continuous Dynamical Systems - B 27, no. 11 (2022). https://doi.org/10.3934/dcdsb.2022009.","ieee":"M. Winkler, “Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities,” Discrete and Continuous Dynamical Systems - B, vol. 27, no. 11, Art. no. 6565, 2022, doi: 10.3934/dcdsb.2022009."},"year":"2022","issue":"11","publication_identifier":{"issn":["1531-3492","1553-524X"]},"publication_status":"published","doi":"10.3934/dcdsb.2022009","title":"Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities","volume":27,"author":[{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"date_created":"2025-12-18T19:30:32Z","date_updated":"2025-12-18T20:05:47Z","publisher":"American Institute of Mathematical Sciences (AIMS)"},{"status":"public","publication":"Discrete and Continuous Dynamical Systems - B","type":"journal_article","language":[{"iso":"eng"}],"_id":"63330","user_id":"31496","year":"2020","intvolume":" 25","page":"4383-4396","citation":{"apa":"Li, G., Tao, Y., & Winkler, M. (2020). Large time behavior in a predator-prey system with indirect pursuit-evasion interaction. Discrete and Continuous Dynamical Systems - B, 25(11), 4383–4396. https://doi.org/10.3934/dcdsb.2020102","short":"G. Li, Y. Tao, M. Winkler, Discrete and Continuous Dynamical Systems - B 25 (2020) 4383–4396.","bibtex":"@article{Li_Tao_Winkler_2020, title={Large time behavior in a predator-prey system with indirect pursuit-evasion interaction}, volume={25}, DOI={10.3934/dcdsb.2020102}, number={11}, journal={Discrete and Continuous Dynamical Systems - B}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Li, Genglin and Tao, Youshan and Winkler, Michael}, year={2020}, pages={4383–4396} }","mla":"Li, Genglin, et al. “Large Time Behavior in a Predator-Prey System with Indirect Pursuit-Evasion Interaction.” Discrete and Continuous Dynamical Systems - B, vol. 25, no. 11, American Institute of Mathematical Sciences (AIMS), 2020, pp. 4383–96, doi:10.3934/dcdsb.2020102.","ama":"Li G, Tao Y, Winkler M. Large time behavior in a predator-prey system with indirect pursuit-evasion interaction. Discrete and Continuous Dynamical Systems - B. 2020;25(11):4383-4396. doi:10.3934/dcdsb.2020102","ieee":"G. Li, Y. Tao, and M. Winkler, “Large time behavior in a predator-prey system with indirect pursuit-evasion interaction,” Discrete and Continuous Dynamical Systems - B, vol. 25, no. 11, pp. 4383–4396, 2020, doi: 10.3934/dcdsb.2020102.","chicago":"Li, Genglin, Youshan Tao, and Michael Winkler. “Large Time Behavior in a Predator-Prey System with Indirect Pursuit-Evasion Interaction.” Discrete and Continuous Dynamical Systems - B 25, no. 11 (2020): 4383–96. https://doi.org/10.3934/dcdsb.2020102."},"publication_identifier":{"issn":["1531-3492","1553-524X"]},"publication_status":"published","issue":"11","title":"Large time behavior in a predator-prey system with indirect pursuit-evasion interaction","doi":"10.3934/dcdsb.2020102","publisher":"American Institute of Mathematical Sciences (AIMS)","date_updated":"2025-12-18T20:00:40Z","volume":25,"date_created":"2025-12-18T19:38:22Z","author":[{"full_name":"Li, Genglin","last_name":"Li","first_name":"Genglin"},{"last_name":"Tao","full_name":"Tao, Youshan","first_name":"Youshan"},{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}]},{"publisher":"American Institute of Mathematical Sciences (AIMS)","date_created":"2022-12-21T09:46:50Z","title":"Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals","issue":"4","year":"2017","keyword":["Applied Mathematics","Discrete Mathematics and Combinatorics"],"language":[{"iso":"eng"}],"publication":"Discrete & Continuous Dynamical Systems - B","date_updated":"2022-12-21T10:05:19Z","volume":22,"author":[{"full_name":"Black, Tobias","id":"23686","last_name":"Black","orcid":"0000-0001-9963-0800","first_name":"Tobias"}],"doi":"10.3934/dcdsb.2017061","publication_identifier":{"issn":["1553-524X"]},"publication_status":"published","page":"1253-1272","intvolume":" 22","citation":{"bibtex":"@article{Black_2017, title={Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals}, volume={22}, DOI={10.3934/dcdsb.2017061}, number={4}, journal={Discrete & Continuous Dynamical Systems - B}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Black, Tobias}, year={2017}, pages={1253–1272} }","short":"T. Black, Discrete & Continuous Dynamical Systems - B 22 (2017) 1253–1272.","mla":"Black, Tobias. “Global Existence and Asymptotic Stability in a Competitive Two-Species Chemotaxis System with Two Signals.” Discrete & Continuous Dynamical Systems - B, vol. 22, no. 4, American Institute of Mathematical Sciences (AIMS), 2017, pp. 1253–72, doi:10.3934/dcdsb.2017061.","apa":"Black, T. (2017). Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals. Discrete & Continuous Dynamical Systems - B, 22(4), 1253–1272. https://doi.org/10.3934/dcdsb.2017061","ama":"Black T. Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals. Discrete & Continuous Dynamical Systems - B. 2017;22(4):1253-1272. doi:10.3934/dcdsb.2017061","chicago":"Black, Tobias. “Global Existence and Asymptotic Stability in a Competitive Two-Species Chemotaxis System with Two Signals.” Discrete & Continuous Dynamical Systems - B 22, no. 4 (2017): 1253–72. https://doi.org/10.3934/dcdsb.2017061.","ieee":"T. Black, “Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals,” Discrete & Continuous Dynamical Systems - B, vol. 22, no. 4, pp. 1253–1272, 2017, doi: 10.3934/dcdsb.2017061."},"_id":"34663","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"user_id":"23686","type":"journal_article","status":"public"}]