Electron. J. Differential Equations, Vol. 2020 (2020), No. 106, pp. 1-26.

Exponential decay and blow-up for nonlinear heat equations with viscoelastic terms and Robin-Dirichlet conditions

Le Thi Phuong Ngoc, Nguyen Thanh Long

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.

Submitted November 20, 2019. Published October 26, 2020.
Math Subject Classifications: 34B60, 35K55, 35Q72, 80A30.
Key Words: Nonlinear heat equations; blow up; exponential decay.

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Le Thi Phuong Ngoc
University of Khanh Hoa
01 Nguyen Chanh Str., Nha Trang City, Vietnam
email: ngoc1966@gmail.com
Nguyen Thanh Long
Department of Mathematics and Computer Science
University of Science
Ho Chi Minh City, Vietnam
email: longnt2@gmail.com

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