Nonautonomous semilinear second order evolution equations with generalized Wentzell boundary conditions

Of concern are the initial-boundary value problems for nonautonomous semilinear second order evolution equations with generalized Wentzell boundary conditions. We succeed in establishing a global wellposedness theorem (in a classical sense) for these problems via a specifically designed operator theoretic approach. Moreover, we obtain sharp estimations for the evolution of the solution along the characteristic curves, which enable us to derive the uniform exponential decay of the associated energies. The results obtained in this paper are still new even for the autonomous case.