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

Wang, Yi; Xiao, Jianwei; Zhou, Dun

doi:10.1090/proc/14386

Spatial-homogeneity of stable solutions of almost-periodic parabolic equations with concave nonlinearity
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by Yi Wang, Jianwei Xiao and Dun Zhou

Proc. Amer. Math. Soc. 147 (2019), 2533-2543

DOI: https://doi.org/10.1090/proc/14386

Published electronically: February 14, 2019

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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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