Stability of planar waves in mono-stable reaction-diffusion equations
Guangying Lv, Mingxin Wang · Proceedings of the American Mathematical Society · 2011
This paper is concerned with the asymptotic stability of planar waves in mono-stable reaction-diffusion equations in $\mathbb {R}^n$, where $n\geq 2$. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar waves as $t\rightarrow \infty$. The convergence is uniform in $\mathbb {R}^n$.