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Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term. (English) Zbl 1049.35047

For the wave equation with a source term \[ u_{tt}- \Delta u = | u| ^{p}u \quad \text{in } \Omega \times (0,\infty) \] it is proved the existence and uniform decay rates of the energy by assuming a nonlinear feedback \(\beta(u_{t})\) acting on the boundary provided that \(\beta\) has necessarily not a polynomial growth near the origin.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
35L70 Second-order nonlinear hyperbolic equations
35B37 PDE in connection with control problems (MSC2000)
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