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• W3184173251 abstract "<p style='text-indent:20px;'>This paper deals with the dynamical properties of the quasilinear parabolic-parabolic chemotaxis system</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE1> begin{document}$ begin{eqnarray*} left{ begin{array}{llll} u_{t} = nablacdot(D(u)nabla u)-chinablacdot(frac{u}{v} nabla v)+mu u- mu u^{2}, , , , &amp;xinOmega, , , , t&gt;0, v_{t} = Delta v-v+u, &amp;xinOmega, , , , t&gt;0, end{array} right. end{eqnarray*} $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>under homogeneous Neumann boundary conditions in a convex bounded domain <inline-formula><tex-math id=M1>begin{document}$ Omegasubsetmathbb{R}^{n} $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=M2>begin{document}$ ngeq2 $end{document}</tex-math></inline-formula>, with smooth boundary. <inline-formula><tex-math id=M3>begin{document}$ chi&gt;0 $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=M4>begin{document}$ mu&gt;0 $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=M5>begin{document}$ D(u) $end{document}</tex-math></inline-formula> is supposed to satisfy the behind properties</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE2> begin{document}$ begin{equation*} begin{split} D(u)geq (u+1)^{alpha} , , , text{with}, , , alpha&gt;0. end{split} end{equation*} $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>It is shown that there is a positive constant <inline-formula><tex-math id=M6>begin{document}$ m_{*} $end{document}</tex-math></inline-formula> such that</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE3> begin{document}$ begin{equation*} begin{split} int_{Omega}ugeq m_{*} end{split} end{equation*} $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>for all <inline-formula><tex-math id=M7>begin{document}$ tgeq0 $end{document}</tex-math></inline-formula>. Moreover, we prove that the solution is globally bounded. Finally, it is asserted that the solution exponentially converges to the constant stationary solution <inline-formula><tex-math id=M8>begin{document}$ (1, 1) $end{document}</tex-math></inline-formula>.</p>" @default.
• W3184173251 created "2021-08-02" @default.
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• W3184173251 date "2022-01-01" @default.
• W3184173251 modified "2023-09-25" @default.
• W3184173251 title "A quasilinear parabolic-parabolic chemotaxis model with logistic source and singular sensitivity" @default.
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• W3184173251 doi "https://doi.org/10.3934/dcdsb.2021193" @default.
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