Displaying similar documents to “Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary.”

Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation

Jong Yeoul Park, Sun Hye Park (2006)

Czechoslovak Mathematical Journal

Similarity:

We consider the damped semilinear viscoelastic wave equation u ' ' - Δ u + 0 t h ( t - τ ) div { a u ( τ ) } d τ + g ( u ' ) = 0 in Ω × ( 0 , ) with nonlocal boundary dissipation. The existence of global solutions is proved by means of the Faedo-Galerkin method and the uniform decay rate of the energy is obtained by following the perturbed energy method provided that the kernel of the memory decays exponentially.