Global bounded solution of the higher-dimensional forager-exploiter model with/without growth sources

Abstract

We investigate the higher-dimensional forager-exploiter model with homogeneous Neumann boundary conditionwhere Ω ⊂ R n is a bounded domain, the constants χ, ξ, λ, µ are positive, m, l > 1 andIt will be shown that, for η 1 = η 2 = 0 and n ≥ 2, on the one hand, there is ε > 0 such that, ifthen this system is globally solvable in the classical sense; On the other hand, the weak taxis effects rule out any blow-up. Secondly, for η 1 > 0, m ≥ 2, η 2 = 0 and n = 2, we establish the global solvability of this problem provided only ξ is sufficiently small. Finally, when n = 2, η 1 , η 2 > 0, we find a condition for the logistic degradation rates m, l that ensures the global existence of the classical solutions.