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

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.

preprint2009arXivOpen access
Pierre CornilleauSerge Nicaise
math.OC
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Open access2 authors1 topic
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Pierre CornilleauSerge Nicaise

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