Existence and uniform decay of the wave equation with nonlinear boundary damping and boundary memory source term

摘要

We consider the nonlinear model of the wave equation y_(tt) - Δy + f_0 (▽y) = 0 subject to the following nonlinear boundary conditions (partial deriv)y/(partial deriv)v + g(y_t) = ∫_0~t h(t-τ)f_1(y(τ)) d_τ. We show existence of solutions by means of Faedo-Galerkin method and the uniform decay is obtained by using the multiplier technique.