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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stability of planar waves in mono-stable reaction-diffusion equations


Authors: Guangying Lv and Mingxin Wang
Journal: Proc. Amer. Math. Soc. 139 (2011), 3611-3621
MSC (2010): Primary 35B35; Secondary 35K57
Published electronically: February 18, 2011
MathSciNet review: 2813391
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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\geq2$. 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$.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10767-6
PII: S 0002-9939(2011)10767-6
Keywords: Traveling wave fronts, stability, upper and lower solutions, reaction-diffusion equation.
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$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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.