Stability of higher-level energy norms of strong solutions to a wave equation with localized nonlinear damping and a nonlinear source term

@inproceedings{Lasiecka2007StabilityOH,
  title={Stability of higher-level energy norms of strong solutions to a wave equation with localized nonlinear damping and a nonlinear source term},
  author={Irena Lasiecka and Daniel Toundykov},
  year={2007}
}
We derive global in time a priori bounds on higherlevel energy norms of strong solutions to a semilinear wave equation: in particular, we prove that despite the influence of a nonlinear source, the evolution of a smooth initial state is globally bounded in the strong topology ∼ H × H. And the bound is uniform with respect to the corresponding norm of the initial data. It is known that an m-accretive semigroup generator monotonically propagates smoothness of the initial condition; however, this… CONTINUE READING
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