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

2019/08/29 by Novrianti, Sawada, O., Tsuge, N.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1908.11050

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.

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