Global generalized solutions to the forager-exploiter model with logistic growth

Abstract

<p style='text-indent:20px;'>This paper presents the global existence of the generalized solutions for the forager-exploiter model with logistic growth under appropriate regularity assumption on the initial value. This result partially generalizes previously known ones.</p>

Depleting the signal: Analysis of chemotaxis‐consumption models—A survey

“…Apart from that, the inclusion of additional relaxation mechanisms, such as saturation effects in nutrient consumption or taxis, nonlinear strengthening of diffusion at large densities of foragers and exploiters, or also logistic‐type growth restrictions, has been found to ensure global existence of solutions within various concepts of solvability also in higher‐dimensional domains (Refs. 124–132). Solutions are known to stabilize to semitrivial homogeneous equilibria, both in the one‐dimensional version () and in some of its modified variants in higher‐dimensional cases, if adequate assumptions are imposed either on smallness of the initial data or r , or on strength of the respective relaxation mechanisms (Refs.…”

“…. Apart from that, the inclusion of additional relaxation mechanisms, such as saturation effects in nutrient consumption or taxis, nonlinear strengthening of diffusion at large densities of foragers and exploiters, or also logistic-type growth restrictions, has been found to ensure global existence of solutions within various concepts of solvability also in higher-dimensional domains (Refs [124][125][126][127][128][129][130][131][132]…”