Traveling wave solutions for time periodic reaction-diffusion systems. (English) Zbl 1397.35057
Summary: This paper deals with traveling wave solutions for time periodic reaction-diffusion systems. The existence of traveling wave solutions is established by combining the fixed point theorem with super- and sub-solutions, which reduces the existence of traveling wave solutions to the existence of super- and sub-solutions. The asymptotic behavior is determined by the stability of periodic solutions of the corresponding initial value problems. To illustrate the abstract results, we investigate a time periodic Lotka-Volterra system with two species by presenting the existence and nonexistence of traveling wave solutions, which connect the trivial steady state to the unique positive periodic solution of the corresponding kinetic system.
MSC:
| 35C07 | Traveling wave solutions |
| 45C05 | Eigenvalue problems for integral equations |
| 45M05 | Asymptotics of solutions to integral equations |
| 92D40 | Ecology |
| 35B10 | Periodic solutions to PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35K57 | Reaction-diffusion equations |
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