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Global attractor for a semilinear pseudoparabolic equation with infinite delay

Dang Thi Phuong Thanh
대한수학회 (The Korean Mathematical Society)|2017.07|대한수학회논문집 (Communications of the KMS)|제32권 제3호|pp. 579-600

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키워드

stabilityweak solutionglobal attractorcompactness methodstationary solutionpseudoparabolic equationenergy method
주제분류수학

초록

In this paper we consider a semilinear pseudoparabolic equation with polynomial nonlinearity and infinite delay. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we prove the existence of a compact global attractor for the continuous semigroup associated to the equation. The existence and exponential stability of weak stationary solutions are also investigated.

Abstract

In this paper we consider a semilinear pseudoparabolic equation with polynomial nonlinearity and infinite delay. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we prove the existence of a compact global attractor for the continuous semigroup associated to the equation. The existence and exponential stability of weak stationary solutions are also investigated.

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