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Commun. Korean Math. Soc. 2017; 32(3): 579-600
Online first article June 22, 2017 Printed July 31, 2017
https://doi.org/10.4134/CKMS.c160142
Copyright © The Korean Mathematical Society.
Global attractor for a semilinear pseudoparabolic equation with infinite delay
Dang Thi Phuong Thanh
Hung Vuong University
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.
Keywords: pseudoparabolic equation, global attractor, stability, weak solution, stationary solution, compactness method, energy method
MSC numbers: 35B41, 35K65, 35D05
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