Behaviors of the energy of solutions of two coupled wave equations with nonlinear damping on a compact manifold with boundary

2017/03/01 by Moez Daoulatli, Daoulatli, M.
Computer Science · Engineering · Mathematics · #35B35 #35L05 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1703.00172

openalex publication_date 2017/03/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this paper we study the behaviors of the the energy of solutions of coupled wave equations on a compact manifold with boundary in the case of indirect nonlinear damping . Only one of the two equations is directly damped by a localized nonlinear damping term. Under geometric conditions on both the coupling and the damping regions we prove that the rate of decay of the energy of smooth solutions of the system is determined from a first order differential equation .

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