Corpus ID: 227209625

Uniform decay rate estimates for the wave equation with subcritical semilinearities and locally distributed nonlinear dissipation.

@article{Cavalcanti2020UniformDR,
  title={Uniform decay rate estimates for the wave equation with subcritical semilinearities and locally distributed nonlinear dissipation.},
  author={Marcelo Moreira Cavalcanti and Val{\'e}ria N. Domingos Cavalcanti and Victor H. Gonzalez Martinez and Turker Ozsari},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}
We study the stabilization and the wellposedness of solutions of the wave equation with subcritical semilinearities and locally distributed nonlinear dissipation. The novelty of this paper is that we deal with the difficulty that the main equation does not have good nonlinear structure amenable to a direct proof of a priori bounds and a desirable observability inequality. It is well known that observability inequalities play a critical role in characterizing the long time behaviour of solutions… Expand

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