Global existence and boundedness of solutions to a\n chemotaxis-consumption model with singular sensitivity

2018/05/23 by Johannes Lankeit, Lankeit, Johannes, Giuseppe Viglialoro +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #35A01 #35K51 #35K55 #35Q92 #92C17 #Analysis of PDEs (math.AP) #Cellular Mechanics and Interactions #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.1805.09193

openalex publication_date 2018/05/23 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

In this paper we study the zero-flux chemotaxis-system n
begincases u_t=
Delta u -
chi
nabla
cdot (
fracuv
nabla v)

\nv_t=
Delta v-f(u)v
endcases in a smooth and bounded domain\n\Ω of \ℝ², with \χ>0 and f\∈ C¹(\ℝ)\nessentially behaving like u^\β, 0<\β<1. Precisely for \χ<1 and\nany sufficiently regular initial data u(x,0)\≥ 0 and v(x,0)>0 on\n\\Ω, we show the existence of global classical solutions. Moreover,\nif additionally m:=\∫_\Ω u(x,0) is sufficiently small, then also their\nboundedness is achieved.\n

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