Weighted Stepanov-Like Pseudo Almost Automorphic Solutions for Evolution Equations and Applications

In this paper, the existence and stability of (weighted) Stepanov-like pseudo almost automorphic solutions are proved for a large class of linear and semilinear evolution equations in interpolation spaces. Our method is based on the one hand on a combination of differential inequalities and interpol...

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Bibliographic Details
Published in:Acta mathematica vietnamica 2021-03, Vol.46 (1), p.103-122
Main Authors: Huy, Nguyen Thieu, Ha, Vu Thi Ngoc, Sac, Le The, Xuan, Pham Truong
Format: Article
Language:English
Subjects:
Differential equations
Fluid dynamics
Fluid flow
Incompressible flow
Interpolation
Linear equations
Linear evolution equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Viscous fluids
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Summary:In this paper, the existence and stability of (weighted) Stepanov-like pseudo almost automorphic solutions are proved for a large class of linear and semilinear evolution equations in interpolation spaces. Our method is based on the one hand on a combination of differential inequalities and interpolations functors for the case of linearized equation, and on the other hand on the fixed point argument for the semi-linear equations to handle the case of (weighted) Stepanov-like pseudo almost automorphic functions. Finally, we apply the abstract results to various problems of incompressible viscous fluid flows.
ISSN:0251-4184
2315-4144
DOI:10.1007/s40306-020-00385-z