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Energy decay for solutions of the wave equation with general memory boundary conditions. (English) Zbl 1240.35328

From the authors’s abstact: “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.”

MSC:

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