Transition Fronts of Combustion Reaction Diffusion Equations in $$\mathbb {R}^{N}$$RN
| Autor: | Hongjun Guo, Zhi-Cheng Wang, Zhen-Hui Bu |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Partial differential equation
010102 general mathematics Mathematical analysis Combustion 01 natural sciences 010101 applied mathematics Planar Monotone polygon Ordinary differential equation Uniqueness 0101 mathematics Diffusion (business) Nonlinear Sciences::Pattern Formation and Solitons Analysis Mathematics |
| Zdroj: | Journal of Dynamics and Differential Equations. 31:1987-2015 |
| ISSN: | 1572-9222 1040-7294 |
| Popis: | This paper is concerned with combustion transition fronts in $$\mathbb {R}^{N}$$$$(N\ge 1)$$. Firstly, we prove the existence and the uniqueness of the global mean speed which is independent of the shape of the level sets of the fronts. Secondly, we show that the planar fronts can be characterized in the more general class of almost-planar fronts. Thirdly, we show the existence of new types of transitions fronts in $$\mathbb {R}^{N}$$ which are not standard traveling fronts. Finally, we prove that all transition fronts are monotone increasing in time, whatever shape their level sets may have. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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