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Spatial-homogeneity of stable solutions of almost-periodic parabolic equations with concave nonlinearity


Authors: Yi Wang, Jianwei Xiao and Dun Zhou
Journal: Proc. Amer. Math. Soc. 147 (2019), 2533-2543
MSC (2010): Primary 35K57, 37B55; Secondary 35B15, 35B40, 34D20
DOI: https://doi.org/10.1090/proc/14386
Published electronically: February 14, 2019
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Abstract | References | Similar Articles | Additional Information

Abstract: We investigate the spatial-homogeneity of stable solutions of
almost-periodic parabolic equations. It is shown that if the nonlinearity satisfies a concave or convex condition, then any linearly stable almost automorphic solution is spatially homogeneous and, moreover, the frequency module of the solution is contained in that of the nonlinearity.


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Additional Information

Yi Wang
Affiliation: School of Mathematical Science, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China

Jianwei Xiao
Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720-3840

Dun Zhou
Affiliation: School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu, 210094, People’s Republic of China
Email: zhd1986@mail.ustc.edu.cn, zhoudun@njust.edu.cn

DOI: https://doi.org/10.1090/proc/14386
Received by editor(s): April 21, 2018
Received by editor(s) in revised form: August 9, 2018, and August 29, 2018
Published electronically: February 14, 2019
Additional Notes: The first author was partially supported by NSF of China Nos. 11825106, 11771414, and 11471305 and Wu Wen-Tsun Key Laboratory.
The third author is the corresponding author and was partially supported by NSF of China No. 11601498 and the Fundamental Research Funds for the Central Universities No. 30918011339.
Communicated by: Wenxian Shen
Article copyright: © Copyright 2019 American Mathematical Society