In this paper we consider the asymptotic stability of the solutions to the nonlinear damped wave equation in 2-D of space. In particular we deal with initial data which are small perturbation (in Sobolev norms) of a self- similar plane diffusive profile which solve a related parabolic equation. The results are achieved by using the classical energy method and in addition we provide polynomial rates of convergences.
Asymptotic stability of plane diffusion waves for the 2-D quasilinear wave equation
LATTANZIO, CORRADO;MARCATI, PIERANGELO
1999-01-01
Abstract
In this paper we consider the asymptotic stability of the solutions to the nonlinear damped wave equation in 2-D of space. In particular we deal with initial data which are small perturbation (in Sobolev norms) of a self- similar plane diffusive profile which solve a related parabolic equation. The results are achieved by using the classical energy method and in addition we provide polynomial rates of convergences.File in questo prodotto:
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