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Acta Mathematica Vietnamica

, Volume 44, Issue 4, pp 875–892 | Cite as

Asymptotic Behavior of Solutions to Semilinear Parabolic Equations with Infinite Delay

  • Dang Thi Phuong ThanhEmail author
Article
  • 24 Downloads

Abstract

We consider a class of semilinear parabolic equations with infinite delay and nonlinearity of polynomial type. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we show the existence of a compact global attractor for the continuous semigroup associated to the problem. The existence and exponential stability of weak stationary solutions are also investigated.

Keywords

Semilinear parabolic equation Infinite delay Weak solution Global attractor Stationary solution Stability 

Mathematics Subject Classification (2010)

35B41 35B35 35D30 35K90 

Notes

Acknowledgements

The author would like to thank Cung The Anh for stimulating discussions on the subject of the paper.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsHung Vuong UniversityViet TriVietnam

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