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- W2918195999 abstract "This paper deals with the quasilinear degenerate chemotaxis system with flux limitation begin{align*} begin{cases} u_t = nablacdotleft(dfrac{u^p nabla u}{sqrt{u^2 + |nabla u|^2}} right) -chi nablacdotleft( dfrac{u^qnabla v}{sqrt{1 + |nabla v|^2}}right), &xin Omega, t>0, [1mm] 0 = Delta v - mu + u, &xin Omega, t>0, end{cases} end{align*} where $Omega := B_R(0) subset mathbb{R}^n$ ($n in mathbb{N}$) is a ball with some $R>0$, and $chi >0$, $p,qgeq1$, $mu := frac 1{|Omega|} int_Omega u_0$ and $u_0$ is an initial data of an unknown function $u$. Bellomo--Winkler (Trans. Amer. Math. Soc. Ser. B;2017;4;31--67) established existence of an initial data such that the corresponding solution blows up in finite time when $p=q=1$. This paper gives existence of blow-up solutions under some condition for $chi$ and $u_0$ when $1leq pleq q$." @default.
- W2918195999 created "2019-03-11" @default.
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- W2918195999 date "2019-02-28" @default.
- W2918195999 modified "2023-09-24" @default.
- W2918195999 title "Finite-time blow-up in a quasilinear degenerate chemotaxis system with flux limitation" @default.
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- W2918195999 doi "https://doi.org/10.48550/arxiv.1903.00125" @default.
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