Asymptotic Behaviors of Global Solutions to Fourth-order Parabolic and Hyperbolic Equations with Dirichlet Boundary Conditions

Wenlong Wu; Yanyan Zhang

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arXiv · 2603.07042

Asymptotic Behaviors of Global Solutions to Fourth-order Parabolic and Hyperbolic Equations with Dirichlet Boundary Conditions

Wenlong Wu·Yanyan Zhang

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Abstract

This paper investigates the asymptotic behaviors of global solutions to fourth-order parabolic and hyperbolic equations with Dirichlet boundary conditions. The equations model Micro-Electro-Mechanical Systems (MEMS) and are depending on a positive voltage parameter $\lambda$. We establish the convergence of global solutions to an equilibrium, along with the convergence rate estimates. Supporting numerical simulations are presented.

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Wenlong Wu, Yanyan Zhang. 2026-03-07. Asymptotic Behaviors of Global Solutions to Fourth-order Parabolic and Hyperbolic Equations with Dirichlet Boundary Conditions. https://arxiv.org/abs/2603.07042

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