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
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Sprache:	eng
Schlagworte:	Asymptotic properties Delay Galerkin method Mathematical analysis Mathematics Mathematics and Statistics Polynomials
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description	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.
doi_str_mv	10.1007/s40306-018-0289-5
format	Article
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title	Asymptotic Behavior of Solutions to Semilinear Parabolic Equations with Infinite Delay
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