Local well posedness for strongly damped wave equations with critical nonlinearities.(English)Zbl 1020.35059

Summary: The strongly damped wave equation is considered and a local well-posedness result is obtained in the product space $$H^1_0(\Omega)\times L^2(\Omega)$$. 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.

MSC:

 35L70 Second-order nonlinear hyperbolic equations 35L20 Initial-boundary value problems for second-order hyperbolic equations 35A07 Local existence and uniqueness theorems (PDE) (MSC2000) 47D06 One-parameter semigroups and linear evolution equations
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References:

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