Lp estimates of solutions to some non-linear wave equations in one space dimension
by Alain Haraux
International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO), Vol. 1, No. 1/2, 2009

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.

Online publication date: Wed, 09-Dec-2009

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