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Global solutions of a doubly tactic resource consumption model with logistic source

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 Added by Jianping Wang
 Publication date 2021
  fields
and research's language is English
 Authors Jianping Wang




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We study a doubly tactic resource consumption model bess left{begin{array}{lll} u_t=tr u- ablacd(u abla w),[1mm] v_t=tr v- ablacd(v abla u)+v(1-v^{beta-1}),[1mm] w_t=tr w-(u+v)w-w+r end{array}right. eess in a smooth bounded domain $ooinR^2$ with homogeneous Neumann boundary conditions, where $rin C^1(barOmegatimes[0,infty))cap L^infty(Omegatimes(0,infty))$ is a given nonnegative function fulfilling bess int_t^{t+1}ii| nsqrt{r}|^2<yy for all t>0. eess It is shown that, firstly, if $beta>2$, then the corresponding Neumann initial-boundary problem admits a global bounded classical solution. Secondly, when $beta=2$, the Neumann initial-boundary problem admits a global generalized solution.



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This paper investigates a high-dimensional chemotaxis system with consumption of chemoattractant begin{eqnarray*} left{begin{array}{l} u_t=Delta u- ablacdot(u abla v), v_t=Delta v-uv, end{array}right. end{eqnarray*} under homogeneous boundary conditions of Neumann type, in a bounded convex domain $Omegasubsetmathbb{R}^n~(ngeq4)$ with smooth boundary. It is proved that if initial data satisfy $u_0in C^0(overline{Omega})$ and $v_0in W^{1,q}(Omega)$ for some $q>n$, the model possesses at least one global renormalized solution.
64 - R. B. Salako , W. Shen 2019
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