Global existence and boundedness of solutions to a two-dimensional forager-exploiter model with/without logistic source

This paper is focused on the zero-flux initial–boundary value problem for a forager-exploiter model of the form ut=Δu−∇⋅(u∇w)+μ1(u−um),x∈Ω,t>0,vt=Δv−∇⋅(v∇u)+μ2(v−vl),x∈Ω,t>0,wt=Δw−f(u)w−g(v)w−μw+r(x,t),x∈Ω,t>0,in a smoothly bounded domain Ω⊂R2, where μ, μ1, μ2, m, l are positive constants,...

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Published inNonlinear analysis: real world applications Vol. 83; p. 104261
Main Authors Zhao, Shengfeng, Xie, Li
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.06.2025
Subjects
Classical solution
Forager-exploiter
Global boundedness
Global existence
secondary 92C17
Forager-exploiter
Global existence
Classical solution
Global boundedness
primary 35B40
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Summary:This paper is focused on the zero-flux initial–boundary value problem for a forager-exploiter model of the form ut=Δu−∇⋅(u∇w)+μ1(u−um),x∈Ω,t>0,vt=Δv−∇⋅(v∇u)+μ2(v−vl),x∈Ω,t>0,wt=Δw−f(u)w−g(v)w−μw+r(x,t),x∈Ω,t>0,in a smoothly bounded domain Ω⊂R2, where μ, μ1, μ2, m, l are positive constants, r(x,t)∈C1(Ω¯×[0,∞))∩L∞(Ω×(0,∞)) is a given nonnegative function, the functions f,g∈C1[0,∞] are assumed to behave essentially like uα, vβ respectively, with some positive constants α and β. It is shown that the initial–boundary value problem possesses globally bounded classical solutions, provided that m≥1 , l≥1, α≤m2 and β<l2.
ISSN:1468-1218
DOI:10.1016/j.nonrwa.2024.104261