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

Abstract

This paper concerns with the global existence and boundedness of classical solution of the higher-dimensional forager–exploiter model with homogeneous Neumann boundary condition and nonnegative initial data. For cases where there are no forager and exploiter growth sources, it will be shown that if either the initial data and the production rate of nutrient are small or the taxis effects are small, then the classical solution exists globally and is bounded. For the case that only the forager has growth source, when [Formula: see text], it will be shown that if the taxis effect of exploiter is small then the classical solution exists globally and is bounded. For the case that both the forager and exploiter have growth restrictions, when [Formula: see text], we find a condition for the logistic degradation rates that ensures the global existence and boundedness of the classical solution.