Boundedness and Almost Periodicity of Solutions for a Class of Semilinear Parabolic Equations with Boundary Degeneracy

Citation:

Yi XIE,Peidong LEI.Boundedness and Almost Periodicity of Solutions for a Class of Semilinear Parabolic Equations with Boundary Degeneracy[J].Chinese Annals of Mathematics B,2020,41(2):303~324
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Authors:

Yi XIE; Peidong LEI

Foundation:

This work was supported by the Guangdong Provincial Natural Science Foundation of China (No.S2013010015800) and the KLSCK of the Ministry of Education of China (No.93K172012K03).
Abstract: In this paper the authors investigate the boundedness and almost periodicity of solutions of semilinear parabolic equations with boundary degeneracy. The equations may be weakly degenerate or strongly degenerate on the lateral boundary. The authors prove the existence, uniqueness and global exponential stability of bounded entire solutions, and also establish the existence theorem of almost periodic solutions if the data are almost periodic.

Keywords:

Almost periodic solution, Bounded entire solution, Boundary degeneracy

Classification:

35K65, 35B15
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