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

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/24980
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