Dispersion for 1-d Schrödinger and wave equations with bv coefficients

In this paper we analyze the dispersion for one dimensional wave and Schrödinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the coefficient showing that dispersion occurs if this variation is small enough b...

Descripción completa

Detalles Bibliográficos
Autores: Beli, N., Ignat, L.I., Zuazua, E.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2016
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/265
Acceso en línea:http://hdl.handle.net/20.500.11824/265
Access Level:acceso abierto
Palabra clave:Schrödinger equation
Wave equation
One space dimension
BV coefficients
Dispersion and Strichartz estimates
Almost periodic functions
Descripción
Sumario:In this paper we analyze the dispersion for one dimensional wave and Schrödinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the coefficient showing that dispersion occurs if this variation is small enough but it may fail when the variation goes beyond a sharp threshold. For the Schrödinger equation we prove that the dispersion holds under the same smallness assumption on the variation of the coefficient. But, whether dispersion may fail for larger coefficients is unknown for the Schrödinger equation.