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Global existence and uniform decay for wave equation with dissipative term and boundary damping. (English) Zbl 1189.35183

Summary: We prove the existence, uniqueness and uniform stability of strong and weak solutions of the nonlinear wave equation \[ u_tt-\Delta u+b(x)u_t+f(u=0 \] in bounded domains with nonlinear damped boundary conditions, given by \[ \frac{\partial u}{\partial v}+g(u_t)=0 \] with restrictions on function \(f(u)\), \(g(ut)\) and \(b(x)\). We prove the existence by means of the Galerkin method and obtain the asymptotic behavior by using of the multiplier technique from the idea of V. Komornik and E. Zuazua [J. Math. Pures Appl., IX. Sér. 69, 33–54 (1990; Zbl 0636.93064)].

MSC:

35L71 Second-order semilinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs

Citations:

Zbl 0636.93064
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References:

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