Published November 3, 2022
| Version v1
Publication
Homogenization and corrector for the wave equation with discontinuous coefficients in time
Description
In this paper we analyze the homogenization of the wave equation with bounded variation
coefficients in time, generalizing the classical result, which assumes Lipschitz-continuity.
We start showing a general existence and uniqueness result for a general sort of hyperbolic
equations. Then, we obtain our homogenization result comparing the solution of a
sequence of wave equations to the solution of a sequence of elliptic ones. We conclude the
paper making an analysis of the corrector. Firstly, we obtain a corrector result assuming
that the derivative of the coefficients in the time variable is equicontinuous. This result
was known for non-time dependent coefficients. After, we show, with a counterexample,
that the regularity hypothesis for the corrector theorem is optimal in the sense that it does
not hold if the time derivative of the coefficients is just bounded.
Additional details
Identifiers
- URL
- https://idus.us.es/handle//11441/138670
- URN
- urn:oai:idus.us.es:11441/138670