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http://dx.doi.org/10.22771/nfaa.2021.26.01.03

LOCAL EXISTENCE AND EXPONENTIAL DECAY OF SOLUTIONS FOR A NONLINEAR PSEUDOPARABOLIC EQUATION WITH VISCOELASTIC TERM  

Nhan, Nguyen Huu (Nguyen Tat Thanh University)
Nhan, Truong Thi (University of Science, Ho Chi Minh City)
Ngoc, Le Thi Phuong (University of Khanh Hoa)
Long, Nguyen Thanh (Department of Mathematics and Computer Science, University of Science)
Publication Information
Nonlinear Functional Analysis and Applications / v.26, no.1, 2021 , pp. 35-64 More about this Journal
Abstract
In this paper, we investigate an initial boundary value problem for a nonlinear pseudoparabolic equation. At first, by applying the Faedo-Galerkin, we prove local existence and uniqueness results. Next, by constructing Lyapunov functional, we establish a sufficient condition to obtain the global existence and exponential decay of weak solutions.
Keywords
Nonlinear pseudoparabolic equation; Neumann-Dirichlet problem; FaedoGalerkin approximation; exponential decay;
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