This paper is concerned with the multidimensional stability of traveling fronts for the combustion and non-KPP monostable equations. Our study contains two parts: in the first part, we first show that the two-dimensional V-shaped traveling fronts are asymptotically stable in $$\mathbb {R}^{n+2}$$ R n + 2 with $$n\ge 1$$ n ≥ 1 under any (possibly large) initial perturbations that decay at space infinity, and then, we prove that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which implies that even very small perturbations to the V-shaped traveling front can lead to permanent oscillation. In the second part, we establish the multidimensional stability of planar traveling front in $$\mathbb {R}^{n+1}$$ R n + 1 with $$n\ge 1$$ n ≥ 1 .
Zeitschrift für angewandte Mathematik und Physik – Springer Journals
Published: Jan 10, 2018
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