[{"citation":{"short":"M. Winkler, Discrete and Continuous Dynamical Systems - B 27 (2022).","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.","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","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","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."},"user_id":"31496","volume":27,"_id":"63312","publisher":"American Institute of Mathematical Sciences (AIMS)","status":"public","type":"journal_article","date_created":"2025-12-18T19:30:32Z","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&gt;\\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&gt;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)&gt;0 $\\end{document}</tex-math></inline-formula>.</p>","lang":"eng"}],"issue":"11","publication":"Discrete and Continuous Dynamical Systems - B","doi":"10.3934/dcdsb.2022009","article_number":"6565","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2025-12-18T20:05:47Z","intvolume":" 27","year":"2022","title":"Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities","author":[{"id":"31496","first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"publication_identifier":{"issn":["1531-3492","1553-524X"]}},{"year":"2020","status":"public","title":"Large time behavior in a predator-prey system with indirect pursuit-evasion interaction","author":[{"first_name":"Genglin","last_name":"Li","full_name":"Li, Genglin"},{"last_name":"Tao","first_name":"Youshan","full_name":"Tao, Youshan"},{"id":"31496","last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael"}],"publication_identifier":{"issn":["1531-3492","1553-524X"]},"publication_status":"published","date_updated":"2025-12-18T20:00:40Z","intvolume":" 25","page":"4383-4396","publisher":"American Institute of Mathematical Sciences (AIMS)","_id":"63330","language":[{"iso":"eng"}],"user_id":"31496","doi":"10.3934/dcdsb.2020102","volume":25,"issue":"11","publication":"Discrete and Continuous Dynamical Systems - B","citation":{"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","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.","short":"G. Li, Y. Tao, M. Winkler, Discrete and Continuous Dynamical Systems - B 25 (2020) 4383–4396.","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.","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","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."},"date_created":"2025-12-18T19:38:22Z","type":"journal_article"},{"intvolume":" 1","publication_status":"published","date_updated":"2022-01-06T06:53:02Z","publication_identifier":{"issn":["1531-3492"]},"author":[{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"first_name":"Oliver","last_name":"Junge","full_name":"Junge, Oliver"},{"full_name":"Thiere, Bianca","last_name":"Thiere","first_name":"Bianca"}],"title":"The numerical detection of connecting orbits","status":"public","year":"2001","volume":1,"user_id":"32829","doi":"10.3934/dcdsb.2001.1.125","language":[{"iso":"eng"}],"_id":"17027","page":"125-135","citation":{"bibtex":"@article{Dellnitz_Junge_Thiere_2001, title={The numerical detection of connecting orbits}, volume={1}, DOI={10.3934/dcdsb.2001.1.125}, number={1531-3492_2001_1_125}, journal={Discrete & Continuous Dynamical Systems - B}, author={Dellnitz, Michael and Junge, Oliver and Thiere, Bianca}, year={2001}, pages={125–135} }","chicago":"Dellnitz, Michael, Oliver Junge, and Bianca Thiere. “The Numerical Detection of Connecting Orbits.” Discrete & Continuous Dynamical Systems - B 1, no. 1531-3492_2001_1_125 (2001): 125–35. https://doi.org/10.3934/dcdsb.2001.1.125.","short":"M. Dellnitz, O. Junge, B. Thiere, Discrete & Continuous Dynamical Systems - B 1 (2001) 125–135.","ama":"Dellnitz M, Junge O, Thiere B. The numerical detection of connecting orbits. Discrete & Continuous Dynamical Systems - B. 2001;1(1531-3492_2001_1_125):125-135. doi:10.3934/dcdsb.2001.1.125","ieee":"M. Dellnitz, O. Junge, and B. Thiere, “The numerical detection of connecting orbits,” Discrete & Continuous Dynamical Systems - B, vol. 1, no. 1531-3492_2001_1_125, pp. 125–135, 2001.","apa":"Dellnitz, M., Junge, O., & Thiere, B. (2001). The numerical detection of connecting orbits. Discrete & Continuous Dynamical Systems - B, 1(1531-3492_2001_1_125), 125–135. https://doi.org/10.3934/dcdsb.2001.1.125","mla":"Dellnitz, Michael, et al. “The Numerical Detection of Connecting Orbits.” Discrete & Continuous Dynamical Systems - B, vol. 1, no. 1531-3492_2001_1_125, 2001, pp. 125–35, doi:10.3934/dcdsb.2001.1.125."},"publication":"Discrete & Continuous Dynamical Systems - B","issue":"1531-3492_2001_1_125","type":"journal_article","date_created":"2020-05-19T20:38:40Z"}]