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In this work, we establish a framework to study the stability of traveling wave solutions for some lattice reaction-diffusion equations. The systems arise from epidemic, biological and many other applied models. Applying different kinds of comparison theorems, we show that all solutions of the Cauchy problem for the lattice differential equations converge exponentially to the traveling wave solutions provided that the initial perturbations around the traveling wave solutions belonging to suitable spaces. Our results can be applied to various discrete reaction-diffusion systems, e.g., the discrete multi-species Lotka-Volterra cooperative model, discrete epidemic model, three-species Lotka-Volterra competitive model, etc.
|Number of pages||18|
|Journal||Discrete and Continuous Dynamical Systems - Series B|
|State||Published - 5 May 2020|
- Comparison theorem
- Lattice reaction-diffusion equations
- Traveling waves
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- 1 Finished
Interaction and Stability of Traveling Waves for Lattice Dynamical System and Reaction-Diffusion Equations(2/3)
1/08/19 → 31/07/20