Asymptotic Behavior of Solutions to Semilinear Parabolic Equations with Infinite Delay

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.

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Acknowledgements

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

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Correspondence to Dang Thi Phuong Thanh.

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Thanh, D.T.P. Asymptotic Behavior of Solutions to Semilinear Parabolic Equations with Infinite Delay. Acta Math Vietnam 44, 875–892 (2019). https://doi.org/10.1007/s40306-018-0289-5

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Keywords

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

Mathematics Subject Classification (2010)

  • 35B41
  • 35B35
  • 35D30
  • 35K90