On a class of nonlinear heat equations with viscoelastic term. (July 2016)

• Record Type: Journal Article
• Authors: Truong, Le Xuan; Y, Nguyen Van
• Is Part Of: Computers & mathematics with applications. Volume 72:issue 1(2016)
• Page Start: 216
• Page End: 232
• Publication Date: 2016-07
• Subjects: Local existence -- Global existence -- Blow-up -- Viscoelastic -- Relaxation function; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.04.044
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: The main goal of this paper is to study a model of the strongly nonlinear heat equation with viscoelastic term and nonlinear interior source of the form { ( 1 + a | u | q − 2 ) u t − Δ u + ∫ 0 t g ( t − s ) Δ u ( s ) d s = f ( u ), in Ω × [ 0, ∞ ), u = 0 on ∂ Ω × [ 0, ∞ ), u ( x, 0 ) = u 0 ( x ) in Ω . We show the results of local (or global) existence of weak solutions by using the Galerkin approximation method. In addition it has been provided sufficient conditions for the large time decay and the finite time blow-up of the weak solutions.