Stability of planar waves in mono-stable reaction-diffusion equations
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- by Guangying Lv and Mingxin Wang PDF
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Abstract:
This paper is concerned with the asymptotic stability of planar waves in mono-stable reaction-diffusion equations in $\mathbb {R}^n$, where $n\geq 2$. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar waves as $t\rightarrow \infty$. The convergence is uniform in $\mathbb {R}^n$.References
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Additional Information
- Guangying Lv
- Affiliation: Department of Mathematics, Southeast University, Nanjing 210018, People’s Republic of China
- Email: gyLvmaths@126.com
- Mingxin Wang
- Affiliation: Science Research Center, Harbin Institute of Technology, Harbin 150080, People’s Republic of China
- Email: mxwang@hit.edu.cn
- Received by editor(s): March 7, 2010
- Received by editor(s) in revised form: March 20, 2010, August 16, 2010, and August 29, 2010
- Published electronically: February 18, 2011
- Additional Notes: The first author is supported by the JSPS Innovation Program CX09$\textrm {B}_{-}$044Z and the Scientific Research Foundation of the Graduate School of Southeast University (YBJJ1009).
The second author is supported by PRC Grants NSFC 10771032 and 11071049. - Communicated by: Yingfei Yi
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 3611-3621
- MSC (2010): Primary 35B35; Secondary 35K57
- DOI: https://doi.org/10.1090/S0002-9939-2011-10767-6
- MathSciNet review: 2813391