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

Pierre Cornilleau; Serge Nicaise

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arXiv · 0902.1823

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

Pierre Cornilleau·Serge Nicaise

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Abstract

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 part of the boundary, where a general borelian 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.

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Pierre Cornilleau, Serge Nicaise. 2009-02-11. Energy decay for solutions of the wave equation with general memory boundary conditions. https://arxiv.org/abs/0902.1823

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