On hyperbolic equations and systems with non-regular time dependent coefficients
journal contributionposted on 2015-08-20, 14:05 authored by Claudia Garetto
In this paper we study higher order weakly hyperbolic equations with time dependent non-regular coefficients. The non-regularity here means less than Hölder, namely bounded coefficients. As for second order equations in  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.
EPSRC First grant EP/L026422/1
- Mathematical Sciences
CitationGARETTO, C., 2015. On hyperbolic equations and systems with non-regular time dependent coefficients. Journal of Differential Equations, 259(11), pp.5846-5874.
Publisher© The Author. Published by Elsevier Inc.
- VoR (Version of Record)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/ by/4.0/
NotesThis is an open access article published by Elsevier under the CC BY license (http://creativecommons.org/licenses/by/4.0/).