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• W4210368445 abstract "<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} u_t = nabla cdot big( D(u) nabla u big) - nabla cdot big( uS(x, u, v)cdot nabla vbig), v_t = Delta v -uv, end{array} right. end{array} $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>is considered in a bounded domain <inline-formula><tex-math id=M1>begin{document}$ Omegasubset mathbb{R}^n $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=M2>begin{document}$ nge 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}^{ntimes 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} qquad {rm{for; all}}; uge 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 Omegatimes (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} qquad {rm{and}};alphain [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>" @default.
• W4210368445 created "2022-02-08" @default.
• W4210368445 creator A5041353240 @default.
• W4210368445 date "2022-01-01" @default.
• W4210368445 modified "2023-10-14" @default.
• W4210368445 title "Approaching logarithmic singularities in quasilinear chemotaxis-consumption systems with signal-dependent sensitivities" @default.
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• W4210368445 doi "https://doi.org/10.3934/dcdsb.2022009" @default.
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