Energy decay in a viscoelastic equation with past history and boundary feedback. Issue 13 (2nd September 2022)

• Record Type: Journal Article
• Authors: Al-Mahdi, Adel M.; Al-Gharabli, Mohammad M.
• Is Part Of: Applicable analysis. Volume 101:Issue 13(2022)
• Page Start: 4743
• Page End: 4758
• Publication Date: 2022-09-02
• Subjects: Y. Ou; Stability -- convex functions -- infinite memory -- viscoelasticity; 35B37 -- 35L55 -- 74D05 -- 93D15 -- 93D20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1869943
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we consider a viscoelastic equation with nonlinear feedback localized on a part of the boundary and in the presence of infinite-memory term. With imposing a more general condition on the relaxation function, we establish a more general stability result that generalizes and improves many earlier results in the literature. Our results are obtained without imposing any restrictive growth assumption on the damping term and without using any assumption on the boundedness of initial data used in many earlier papers in the literature.