Existence of periodic solutions for a nonlinear plate coupling system with thermal memory and external forces

Xia Li; Jiang-Long Shen; Hang-Jing Xiong; Run-Fa  Zhang

doi:10.59400/adecp3876

Existence of periodic solutions for a nonlinear plate coupling system with thermal memory and external forces

Xia Li
School of Mathematics and Physics, Yibin University, Yibin 644000, China
Jiang-Long Shen
School of Mathematics and Physics, Yibin University, Yibin 644000, China
Hang-Jing Xiong
School of Mathematics and Physics, Yibin University, Yibin 644000, China
Run-Fa Zhang
School of Automation and Software Engineering, Shanxi University, Taiyuan 030013, China

Article ID: 3876

DOI: https://doi.org/10.59400/adecp3876

Keywords: thermal memory effect; external force; nonlinear plate coupling system; time-periodic solution

Abstract

This paper is devoted to investigating the existence and uniqueness of T-periodic solutions for a nonlinear thermoelastic plate coupling system with thermal memory effects and time-periodic external forces, derived from the non-Fourier heat flux law—a model more physically realistic for characterizing the thermal response of materials with transient heat conduction behavior. To address the mathematical challenges of this coupled system, we first transform the original high-order system into an equivalent first-order evolution system via auxiliary and memory variable substitutions. Using the Galerkin method to construct finite-dimensional approximate solutions, we then apply the Leray-Schauder fixed-point theorem to prove the existence of approximate periodic solutions, deriving uniform a priori estimates for their derivatives in Hilbert space V 0 via Hölder’s, Poincaré’s, and Gronwall’s inequalities. The Sobolev compact embedding theorem verifies the convergence of approximate solutions, establishing the existence of T-periodic solutions for the original system; uniqueness is further proven via an energy difference functional and Gronwall’s lemma under a smallness condition on external forces. This work enriches the theoretical framework for periodic solutions of memory-type thermoelastic coupling systems and provides a foundation for engineering dynamic analysis of plate structures.

Published

2026-03-10

How to Cite

Li, X., Shen, J.-L., Xiong, H.-J., & Zhang, R.-F. (2026). Existence of periodic solutions for a nonlinear plate coupling system with thermal memory and external forces. Advances in Differential Equations and Control Processes, 33(1). https://doi.org/10.59400/adecp3876

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Vol. 33 No. 1 (2026)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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