Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 106, pp. 1-26.

Title: Exponential decay and blow-up for nonlinear heat equations with
       viscoelastic terms and Robin-Dirichlet conditions
       
Authors: Le Thi Phuong Ngoc (Univ. of Khanh Hoa, Ho Chi Minh City, Vietnam)
         Nguyen Thanh Long (Univ. of Science, Ho Chi Minh City, Vietnam)

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