Multidimensional stability of traveling fronts in combustion and non-KPP monostable equations

Multidimensional stability of traveling fronts in combustion and non-KPP monostable equations 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 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Zeitschrift für angewandte Mathematik und Physik Springer Journals

Multidimensional stability of traveling fronts in combustion and non-KPP monostable equations

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Engineering; Theoretical and Applied Mechanics; Mathematical Methods in Physics
ISSN
0044-2275
eISSN
1420-9039
D.O.I.
10.1007/s00033-017-0906-5
Publisher site
See Article on Publisher Site

Abstract

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 .

Journal

Zeitschrift für angewandte Mathematik und PhysikSpringer Journals

Published: Jan 10, 2018

References

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