On a nonlinear heat equation with viscoelastic term associated with Robin conditions. Issue 16 (10th December 2017)

• Record Type: Journal Article
• Authors: Ngoc, Le Thi Phuong; Y, Nguyen Van; Thuyet, Tran Minh; Long, Nguyen Thanh
• Is Part Of: Applicable analysis. Volume 96:Issue 16(2017)
• Page Start: 2717
• Page End: 2736
• Publication Date: 2017-12-10
• Subjects: Faedo–Galerkin method -- Nonlinear heat equation; Robin conditions; Blow up; Asymptotic behavior of solutions; 34B60 -- 35K55 -- 35Q72 -- 80A30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1238461
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : This paper is devoted to study of a nonlinear heat equation with a viscoelastic term associated with Robin conditions. At first, by the Faedo–Galerkin and the compactness method, we prove existence, uniqueness, and regularity of a weak solution. Next, we prove that any weak solution with negative initial energy will blow up in finite time. Finally, by the construction of a suitable Lyapunov functional, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions.