Lp-asymptotic stability of 1D damped wave equations with localized and linear damping

2021/04/12 by Kafnemer, Meryem, Benmiloud, Mebkhout, Jean, Frédéric +1
#35L05 #93D20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2104.05679

Abstract

In this paper, we study the L^p-asymptotic stability of the one-dimensional linear damped wave equation with Dirichlet boundary conditions in [0,1], with p∈ (1,∞). The damping term is assumed to be linear and localized to an arbitrary open sub-interval of [0,1]. We prove that the semi-group (S_p(t))_{t≥ 0} associated with the previous equation is well-posed and exponentially stable. The proof relies on the multiplier method and depends on whether p≥ 2 or 1

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