This paper is concerned with traveling waves of reaction–diffusion systems. The definition of coupled quasi-upper and quasi-lower solutions is introduced for systems with mixed quasimonotone functions, and the definition of ordered quasi-upper and quasi-lower solutions is also given for systems with quasimonotone nondecreasing functions. By the monotone iteration method, it is shown that if the system has a pair of coupled quasi-upper and quasi-lower solutions, then there exists at least a traveling wave solution. Moreover, if the system has a pair of ordered quasi-upper and quasi-lower solutions, then there exists at least a traveling wavefront. As an application we consider the delayed system of a mutualistic model.
|Journal||Nonlinear Analysis: Theory, Methods & Applications|
|Publication status||Published - 2010|
- Traveling wave
- Mixed quasimonotonicity
- Upper and lower solutions
Lin, Z., Pedersen, M., & Tian, C. (2010). Traveling wave solutions for reaction-diffusion systems. Nonlinear Analysis: Theory, Methods & Applications, 73(10), 3303-3313. https://doi.org/10.1016/j.na.2010.07.010