General decay for a nonlinear Bresse system with memory conditions on part of the boundary

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 on , 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.