Positive solutions to the reaction diffusion equations for prey-predator models with dormancy of predators

TL;DR

This paper proves the global existence and behavior of positive solutions for reaction-diffusion prey-predator models with predator dormancy, using new approximation methods and maximum principles.

Contribution

It introduces novel approximation techniques and applies maximum principles to establish global solutions for complex prey-predator reaction-diffusion systems with dormancy.

Findings

Global existence of positive solutions is established.

Solutions exhibit specific asymptotic behaviors.

Invariant regions are characterized for the system.

Abstract

The time-global unique solvability on the reaction diffusion equations for prey-predator models with density-dependent inhibitor and dormancy on predators is established. The crucial step of the proof is to construct time-local non-negative classical solutions. To do so, new successive approximation and theories of time-evolution operators are used. Due to the maximum principle, the solutions are extended time-globally. Via analysis on the corresponding ordinary differential equations, invariant regions and asymptotic behaviors of solutions are also investigated.