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Nonnegative solutions to the reaction-diffusion equations for prey-predator models with the dormancy of predators
  • Novrianti Novrianti,
  • Okihiro Sawada,
  • Naoki Tsuge
Novrianti Novrianti
Gifu University Faculty of Engineering Graduate School of Engineering
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Okihiro Sawada
Kitami Kogyo Daigaku
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Naoki Tsuge
Gifu University
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Abstract

The time-global unique solvability on the reaction--diffusion equations for preypredator models and dormancy on predators is established. The crucial step is to construct time-local nonnegative classical solutions by using a new approximation associated with time-evolution operators. Although the system does not equip usual comparison principles, a priori bounds are derived, so solutions are extended time-globally. Via observations to the corresponding ordinary differential equations, invariant regions and asymptotic behaviors of solutions are also investigated.

Peer review status:UNDER REVIEW

15 Jan 2021Submitted to Mathematical Methods in the Applied Sciences
16 Jan 2021Assigned to Editor
16 Jan 2021Submission Checks Completed
23 Jan 2021Reviewer(s) Assigned