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

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 ${\mathrm{\Gamma }}_1$, 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.

Keywords:

• Bresse system
• general decay rate
• memory boundary term

AMS Subject Classification (2000):

• 35L70
• 35B40

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11771216], the Key Research and Development Program of Jiangsu Province (Social Development) [grant number BE2019725], the Six Talent Peaks Project in Jiangsu Province [grant number 2015-XCL-020] and the Qing Lan Project of Jiangsu Province; Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology.