Local well posedness for strongly damped wave equations with critical nonlinearities

Abstract

In this article the strongly damped wave equation is considered and a local well posedness result is obtained in the product space H01(Ω) × L2(Ω). The space of initial conditions is chosen according to the energy functional, whereas the approach used in this article is based on the theory of analytic semigroups as well as interpolation and extrapolation spaces. This functional analytic framework allows local existence results to be proved in the case of critically growing nonlinearities, which improves the existing results.