Acta Mathematica Vietnamica
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Asymptotic Behavior of Solutions to Semilinear Parabolic Equations with Infinite Delay
Dang Thi Phuong Thanhpp. 875-892
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.