Differential and Integral Equations

Energy decay for solutions of the wave equation with general memory boundary conditions

Pierre Cornilleau and Serge Nicaise

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We consider the wave equation in a smooth domain subject to Dirichlet boundary conditions on one part of the boundary and dissipative boundary conditions of memory-delay type on the remainder of the boundary, where a general Borel measure is involved. Under quite weak assumptions on this measure, using the multiplier method and a standard integral inequality, we show the exponential stability of the system. Some examples of measures satisfying our hypotheses are given, recovering and extending some of the results from the literature.

Article information

Differential Integral Equations, Volume 22, Number 11/12 (2009), 1173-1192.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L20: Initial-boundary value problems for second-order hyperbolic equations
Secondary: 35B40: Asymptotic behavior of solutions 35L05: Wave equation


Cornilleau, Pierre; Nicaise, Serge. Energy decay for solutions of the wave equation with general memory boundary conditions. Differential Integral Equations 22 (2009), no. 11/12, 1173--1192. https://projecteuclid.org/euclid.die/1356019411

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