Exponential decay and blow-up results for a viscoelastic equation with variable sources. Issue 3 (11th February 2023)

• Record Type: Journal Article
• Authors: Le, Nhan Cong; Le, Truong Xuan; Nguyen, Y. Van
• Is Part Of: Applicable analysis. Volume 102:Issue 3(2023)
• Page Start: 782
• Page End: 799
• Publication Date: 2023-02-11
• Subjects: Nonlinear wave equation -- blow-up -- decay estimate -- variable exponent sources; 35L05 -- 35B44 -- 74Dxx; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1965581
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : This work deals with a class of nonlinear viscoelastic wave equations with strong damping and variable exponent sources. The main interest of this paper compared to many previous works in the literature is able to use the idea of potential well method to study both the finite time blow-up for solutions starting from the unstable sets and decay estimate for global solutions starting in the potential wells.