Exponential decay and blow-up for nonlinear heat equations with viscoelastic terms and Robin-Dirichlet conditions
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Date
2020-10-26
Authors
Ngoc, Le Thi Phuong
Long, Nguyen Thanh
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we consider a system of nonlinear heat equations with viscoelastic terms and Robin-Dirichlet conditions. First, we prove existence and uniqueness of a weak solution. Next, we prove a blow up result of weak solutions with negative initial energy. Also, we give a sufficient condition that guarantees the existence and exponential decay of global weak solutions. The main tools are the Faedo-Galerkin method, a Lyapunov functional, and a suitable energy functional.
Description
Keywords
Nonlinear heat equations, Blow up, Exponential decay
Citation
Ngoc, L. T. P., & Long, N. T. (2020). Exponential decay and blow-up for nonlinear heat equations with viscoelastic terms and Robin-Dirichlet conditions. <i>Electronic Journal of Differential Equations, 2020</i>(106), pp. 1-26.
Rights
Attribution 4.0 International