Exponential decay of solutions of damped wave equations in one dimensional space in the L^p framework for various boundary conditions

2022/12/18 by Yacine Chitour, Chitour, Yacine, Hoài-Minh Nguyên +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2212.09164

openalex publication_date 2022/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the decay of the solutions of the damped wave equations in one dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions where the damping coefficient is a function of space and time. The analysis is based on the study of the corresponding hyperbolic systems associated with the Riemann invariants. The key ingredient in the study of these systems is the use of the internal dissipation energy to estimate the difference of solutions with their mean values in an average sense.

Related

• Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions
• One dimensional wave equation with in-domain localized damping and Wentzell boundary conditions
• Remark on the exponential decay of the solutions of the damped wave equation
• Decay of approximate solutions for the damped semilinear wave equation\n on a bounded 1d domain
• L^p asymptotic stability of 1D damped wave equation with nonlinear distributed damping