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- W3101231361 abstract "In this article we consider a cascaded taxis model for two proliferating and degrading species which thrive on the same nutrient but orient their movement according to different schemes. In particular, we assume the first group, the foragers, to orient their movement directly along an increasing gradient of the food density, while the second group, the exploiters, instead track higher densities of the forager group. Specifically, we will investigate an initial boundary-value problem for a prototypical forager-exploiter model of the form begin{align*} left{ begin{array}{r@{,}c@{,}l@{quad }l@{quad}l@{quad}l@{,}c} u_{t}&=&Delta u-nablacdotbig(unabla wbig)+f(u), &xinOmega,& t>0, v_{t}&=&Delta v-nablacdotbig(vnabla ubig)+g(v), &xinOmega,& t>0, w_{t}&=&Delta w-(u+v)w-mu w+r(x,t), &xinOmega,& t>0, end{array}right. end{align*}%} in a smoothly bounded domain $Omegasubsetmathbb{R}^2$, where $mugeq 0$, $rin C^1(bar{Omega}times[0,infty))cap L^infty!left(Omegatimes(0,infty)right)$ is nonnegative and the functions $f,gin C^1!left([0,infty)right)$ are assumed to satisfy $f(0)geq0$, $g(0)geq0$ as well as $$-k_f s^{alpha} -l_fleq f(s)leq -K_f s^alpha+L_f text{ and } -k_g s^beta -l_gleq g(s)leq -K_g s^beta+L_gquadtext{for }sgeq0,$$ respectively, with constants $alpha,beta>1$, $k_f,K_f,k_g,K_g>0$ and $l_f,L_f,l_g,L_ggeq0$ and $alpha,beta>1$. Assuming that $alpha>1+sqrt{2}$, $min{alpha,beta}>frac{alpha+1}{alpha-1}$ and that $r$ satisfies certain structural conditions we establish the global solvability of this system with respect to a suitable generalized solution concept and then, for the more restrictive case of $alpha,beta>1+sqrt{2}$ and $mu>0$, investigate an eventual regularity effect driven by the decay of the nutrient density $w$." @default.
- W3101231361 created "2020-11-23" @default.
- W3101231361 creator A5033947046 @default.
- W3101231361 date "2020-06-07" @default.
- W3101231361 modified "2023-10-10" @default.
- W3101231361 title "Global generalized solutions to a forager–exploiter model with superlinear degradation and their eventual regularity properties" @default.
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- W3101231361 doi "https://doi.org/10.1142/s0218202520400072" @default.
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