Electron. J. Diff. Equ., Vol. 2015 (2015), No. 254, pp. 1-17.

Traveling curved fronts of bistable reaction-diffusion equations with delay

Xiongxiong Bao, Wen-Hui Huang

Abstract:
This article concerns the existence and stability of traveling curved fronts for bistable reaction-diffusion equations with delay in two-dimensional space. Using the comparison principle and establishing super- and sub- solutions, we prove the existence of traveling curved fronts. We also show that such traveling curved front is unique and stable.

Submitted July 14, 2015. Published September 29, 2015.
Math Subject Classifications: 35C07, 35R10, 35K57.
Key Words: Existence; stability; traveling curved fronts; bistable; reaction-diffusion equation; delay.

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Xiongxiong Bao
School of Mathematics and Statistics
Lanzhou University
Lanzhou, Gansu 730000, China
email: baoxx09@lzu.edu.cn
Wen-Hui Huang
School of Mathematics and Statistics
Lanzhou University
Lanzhou, Gansu 730000, China
email: huangwh10@lzu.edu.cn

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