On hyperbolic equations and systems with non-regular time dependent coefficients
Abstract
In this paper we study higher order weakly hyperbolic equations with time dependent non-regular coefficients. The non-regularity here means less than H\"older, namely bounded coefficients. As for second order equations in \cite{GR:14} we prove that such equations admit a `very weak solution' adapted to the type of solutions that exist for regular coefficients. The main idea in the construction of a very weak solution is the regularisation of the coefficients via convolution with a mollifier and a qualitative analysis of the corresponding family of classical solutions depending on the regularising parameter. Classical solutions are recovered as limit of very weak solutions. Finally, by using a reduction to block Sylvester form we conclude that any first order hyperbolic system with non-regular coefficients is solvable in the very weak sense.
Cite
@article{arxiv.1504.03716,
title = {On hyperbolic equations and systems with non-regular time dependent coefficients},
author = {Claudia Garetto},
journal= {arXiv preprint arXiv:1504.03716},
year = {2015}
}