General decay for a nonlinear Bresse system with memory conditions on part of the boundary. Issue 9 (4th July 2021)

• Record Type: Journal Article
• Authors: Chen, Kewang; Liu, Wenjun; Yu, Jun
• Is Part Of: Applicable analysis. Volume 100:Issue 9(2021)
• Page Start: 1949
• Page End: 1971
• Publication Date: 2021-07-04
• Subjects: Bresse system -- general decay rate -- memory boundary term; 35L70 -- 35B40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1671976
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we study the general decay rate of a nonlinear Bresse system with memory conditions on part of the boundary. Without imposing u 0 = v 0 = w 0 = 0 on Γ 1, an explicit general decay rate results are established under suitable assumptions of the resolvent kernels. It's worth pointing out that our general decay results are not necessarily of exponential-type or polynomial-type, which are also different from the general decay results obtained in Khemmoudj and Hamadouche [General decay of solutions of a Bresse system with viscoelastic boundary conditions. Discrete Contin Dyn Syst. 2017;37(9):4857–4876]. Moreover, our general decay results allow a wider class of relaxation functions and initial data, and thus generalize some previous results existing in the literature.