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

作者：Bu, Zhen-Hui; Wang, Zhi-Cheng^*

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2018, 69(1): 12.

DOI：10.1007/s00033-017-0906-5

• Planar traveling front
• V-shaped traveling front
• Combustion nonlinearity
• Non-KPP monostable nonlinearity
• Multidimensional asymptotic stability

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 Rn+2 with 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 Rn+1 with n >= 1.

• 出版日期2018-2
• 单位兰州大学