Abstract.
We consider the nonlinear model of the wave equation
\(y_{tt}-\Delta y+f_0\left(\nabla y\right)=0\)
subject to the following nonlinear boundary conditions
\(\frac{\partial y}{\partial\nu}+g(y_t)=\int_0^th(t-\tau )f_1(y( \tau ))\,d\tau .\)
We show existence of solutions by means of Faedo-Galerkin method and the uniform decay is obtained by using the multiplier technique.
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Received: 15 June 2000 / Accepted: 4 December 2000 / Published online: 29 April 2002
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Aassila, M., Cavalcanti, M. & Domingos Cavalcanti, V. Existence and uniform decay of the wave equation with nonlinear boundary damping and boundary memory source term. Calc Var 15, 155–180 (2002). https://doi.org/10.1007/s005260100096
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DOI: https://doi.org/10.1007/s005260100096