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Stabilization of the wave equation with variable coefficients and boundary condition of memory type. (English) Zbl 1139.35373

The authors study the stabilization of the wave equation with variable coefficients subject to Dirichlet boundary conditions on one part of the boundary and dissipative conditions of memory type on the remainder part of the boundary. The results obtained are mainly based on the use of differential geometry arguments, on the multiplier method and the introduction of suitable Lyapounov functionals.

MSC:

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