Title: Lp estimates of solutions to some non-linear wave equations in one space dimension

Authors: Alain Haraux

Addresses: UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques Louis Lions, F-75005, Paris, France; CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France

Abstract: Decay estimates like a negative power of t are studied in some general Sobolev spaces for a solution of the one-dimensional semi-linear wave equation with power-like damping term and Dirichlet homogeneous boundary conditions. Upper estimates of this kind are valid for smooth initial data, and we establish also weaker estimates from below on the time-derivative which differ from the above upper estimates by a 3/2 factor with respect to the power of t.

Keywords: Lp estimates; nonlinear wave equations; one dimension.

DOI: 10.1504/IJMMNO.2009.030093

International Journal of Mathematical Modelling and Numerical Optimisation, 2009 Vol.1 No.1/2, pp.146 - 152

Published online: 09 Dec 2009 *

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