Positive solutions to the prey-predator equations with dormancy of predators.
- Resource Type
- Article
- Authors
- Novrianti; Okihiro Sawada; Naoki Tsuge
- Source
- European Journal of Applied Mathematics. Feb2024, Vol. 35 Issue 1, p96-108. 13p.
- Subject
- *LOTKA-Volterra equations
*ORDINARY differential equations
*PARTIAL differential equations
*REACTION-diffusion equations
*PREDATORY animals
*EQUATIONS
- Language
- ISSN
- 0956-7925
The time-global unique classical positive solutions to the reaction-diffusion equations for prey-predator models with dormancy of predators are constructed. The feature appears on the nonlinear terms of Holling type II functional response. The crucial step is to establish time-local positive classical solutions by using a new approximation associated with time-evolution operators. Although the system does not equip usual comparison principle for solutions to partial differential equation, a priori bounds are derived by enclosing and renormalising arguments of solutions to the corresponding ordinary differential equations. Furthermore, time-global existence, invariant regions and asymptotic behaviours of solutions follow from such a priori bounds. [ABSTRACT FROM AUTHOR]