Asymptotic Behavior of Solutions to Semilinear Parabolic Equations with Infinite Delay

Asymptotic Behavior of Solutions to Semilinear Parabolic Equations with Infinite Delay

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...

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Veröffentlicht in:Acta mathematica vietnamica 2019-12, Vol.44 (4), p.875-892
1. Verfasser: Thanh, Dang Thi Phuong
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic properties
Delay
Galerkin method
Mathematical analysis
Mathematics
Mathematics and Statistics
Polynomials
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Zusammenfassung: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.
ISSN:0251-4184
2315-4144
DOI:10.1007/s40306-018-0289-5