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- W4225985220 abstract "<p style='text-indent:20px;'>We consider a parabolic-elliptic system of partial differential equations with a chemotactic term in a <inline-formula><tex-math id=M1>begin{document}$ N $end{document}</tex-math></inline-formula>-dimensional unit ball <inline-formula><tex-math id=M2>begin{document}$ B $end{document}</tex-math></inline-formula> describing the behavior of a biological species <inline-formula><tex-math id=M3>begin{document}$ u $end{document}</tex-math></inline-formula> and a chemical stimuli <inline-formula><tex-math id=M4>begin{document}$ v $end{document}</tex-math></inline-formula>. The system presents a sub-linear dependence of <inline-formula><tex-math id=M5>begin{document}$ nabla v $end{document}</tex-math></inline-formula> in the chemotactic coefficient and a nonlinear diffusive term. The evolution of <inline-formula><tex-math id=M6>begin{document}$ u $end{document}</tex-math></inline-formula> is described by the equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE1> begin{document}$ u_t - Delta u^m = - div (chi u |nabla v|^{p-2} nabla v), quad mbox{ for } m >2, quad p in ( 1,2), quad N geq 1 $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>for a positive constant <inline-formula><tex-math id=M7>begin{document}$ chi $end{document}</tex-math></inline-formula>. The concentration of the chemical substance <inline-formula><tex-math id=M8>begin{document}$ v $end{document}</tex-math></inline-formula> satisfies the linear elliptic equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE2> begin{document}$ - Delta v = u - frac{1}{|B|} int_{B} u_0dx. $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>We consider the radially symmetric case and we prove the local existence of weak solutions for the mass accumulation function under assumption</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE3> begin{document}$ - frac{1}{m}+ frac{1}{N} + 1-frac{pm}{4(m-1)} geq 0, $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>for radial and regular initial data. Additionally, if the constrain</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE4> begin{document}$ frac{m }{m- 2} left[ frac{pm}{2(m-1)}-1right] leq 1 $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>is satisfied, the solution globally exists in time.</p>" @default.
- W4225985220 created "2022-05-05" @default.
- W4225985220 creator A5017913354 @default.
- W4225985220 date "2022-01-01" @default.
- W4225985220 modified "2023-10-14" @default.
- W4225985220 title "Radially symmetric solutions for a Keller-Segel system with flux limitation and nonlinear diffusion" @default.
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- W4225985220 doi "https://doi.org/10.3934/dcdss.2022045" @default.
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