wave-eq-final-05-2020.pdf (412.38 kB)
Download file

On the wave equation with multiplicities and space-dependent irregular coefficients

Download (412.38 kB)
journal contribution
posted on 15.01.2021, 11:51 by Claudia GarettoClaudia Garetto
In this paper we study the well-posedness of the Cauchy problem for a wave equation with multiplicities and space-dependent irregular coefficients. As in \cite{GR:14} in order to give a meaningful notion of solution, we employ the notion of very weak solution, which construction is based on a parameter dependent regularisation of the coefficients via mollifiers. We prove that, even with distributional coefficients, a very weak solution exists for our Cauchy problem and it converges to the classical one when the coefficients are smooth. The dependence on the mollifiers of very weak solutions is investigated at the end of the paper in some instructive examples.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Transactions of the American Mathematical Society

Volume

374

Issue

2021

Pages

3131-3176

Publisher

American Mathematical Society

Version

AM (Accepted Manuscript)

Rights holder

© American Mathematical Society

Publisher statement

First published in Transactions of the American Mathematical Society in 374(2021), pp. 3131-3176, published by the American Mathematical Society

Acceptance date

26/09/2020

Publication date

2021-02-12

Copyright date

2021

ISSN

0002-9947

eISSN

1088-6850

Language

en

Depositor

Dr Claudia Garetto. Deposit date: 14 January 2021