arXiv subjects
Publications and source records attributed to Xin-Tian Zhang.
This paper is concerned with curved fronts of combustion reaction-diffusion equations in $\mathbb{R}^N$ $(N\geq2)$. By mixing finite planar fronts and constructing suitable super- and subsolutions, we prove the existence, uniqueness and stability of polytope-like curved fronts in $\mathbb{R}^N$. Besides, we show that these curved fronts are transition fronts.
This paper is concerned with curved fronts of combustion reaction-diffusion equations in spatially periodic media in $\mathbb{R}^N$ $(N\geq2)$. Under the assumption that there are moving pulsating fronts for any given propagation direction $e \in \mathbb{S}^{N-1}$, and by constructing suitable super- and sub-solutions, we prove the existence of a curved front with polytope-like shape in $\mathbb{R}^N$. Then we show that the curved front is unique and asymptotically stable.