Existence, uniqueness and uniform decay for the nonlinear beam degenerate equation with weak damping

摘要

In this paper we prove global existence and uniqueness of weak solutions of the problem for the nonlinear beam degenerate equationwhereQ is a cylindrical domain of , n⩾1, with the lateral boundary Σ and K(x,t) is a real function defined in Q, K(x,t)⩾0 for all which satisfies some appropriate conditions. M(λ) is a real function such that M(λ)⩾−β, 0<β<λ1, λ1 is the first eigenvalue of the operator Δ2. Moreover, the uniform decay rates of the energy are obtained as time goes to infinity.