Artículo
Homogenization and corrector for the wave equation with discontinuous coefficients in time
Autor/es | Casado Díaz, Juan
Couce Calvo, Julio Maestre, Faustino Martín Gómez, José Domingo |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2011-01-28 |
Fecha de depósito | 2022-11-03 |
Publicado en |
|
Resumen | 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 ... 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. |
Cita | Casado Díaz, J., Couce Calvo, J., Maestre, F. y Martín Gómez, J.D. (2011). Homogenization and corrector for the wave equation with discontinuous coefficients in time. Journal of Mathematical Analysis and Applications, 379 (2), 664-681. https://doi.org/10.1016/j.jmaa.2011.01.054. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
Homogenization and corrector for ... | 280.2Kb | [PDF] | Ver/ | |