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

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- by Claudia Garetto PDF
- Trans. Amer. Math. Soc.
**374**(2021), 3131-3176 Request permission

## Abstract:

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 Garetto and Ruzhansky [Arch. Ration. Mech. Anal. 217 (2015), pp. 113–154], 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.## References

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## Additional Information

**Claudia Garetto**- Affiliation: Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom
- MR Author ID: 729291
- ORCID: 0000-0001-7907-6072
- Email: c.garetto@lboro.ac.uk
- Received by editor(s): May 26, 2020
- Published electronically: February 12, 2021
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**374**(2021), 3131-3176 - MSC (2020): Primary 35L05, 35L15
- DOI: https://doi.org/10.1090/tran/8319
- MathSciNet review: 4237945