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Zeitschrift für Analysis und ihre Anwendungen


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Volume 37, Issue 1, 2018, pp. 51–72
DOI: 10.4171/ZAA/1602

Published online: 2018-01-08

Planar Traveling Waves of Mono-Stable Reaction-Diffusion Equations

Xiaohuan Wang[1]

(1) Henan University, Kaifeng, China

This paper is concerned with planar traveling wavefronts of mono-stable reaction-diffusion equations in $\mathbb{R}^n$ ($n\geq2$). We show that the large time behavior of the disturbed fronts can be controlled by two functions, which are the solutions of the specified nonlinear parabolic equations in $\mathbb{R}^{n-1}$, and the planar traveling fronts are asymptotically stable in $L^\infty(\mathbb{R}^n)$ under ergodic perturbations, which include quasi-periodic and almost periodic ones as special cases.

Keywords: Planar traveling wavefronts, stability, super-solution and sub-solutions, mono-stable reaction-diffusion equations

Wang Xiaohuan: Planar Traveling Waves of Mono-Stable Reaction-Diffusion Equations. Z. Anal. Anwend. 37 (2018), 51-72. doi: 10.4171/ZAA/1602