Dispersion for 1-D Schrödinger and wave equations with BV coefficients

Beli CN, Ignat LI, Zuazua E (2016)

Publication Type: Journal article

Publication year: 2016

Journal

Annales de l'Institut Henri Poincaré - Analyse Non Linéaire Elsevier Masson / Institute Henri Poincaré

Book Volume: 33

Pages Range: 1473-1495

Journal Issue: 6

DOI: 10.1016/j.anihpc.2015.06.002

Abstract

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.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Romanian Academy / Academia Română RO Romania (RO) Basque Center of Applied Mathematics (BCAM) ES Spain (ES)

How to cite

APA:

Beli, C.N., Ignat, L.I., & Zuazua, E. (2016). Dispersion for 1-D Schrödinger and wave equations with BV coefficients. Annales de l'Institut Henri Poincaré - Analyse Non Linéaire, 33(6), 1473-1495. https://dx.doi.org/10.1016/j.anihpc.2015.06.002

MLA:

Beli, Constantin N., Liviu I. Ignat, and Enrique Zuazua. "Dispersion for 1-D Schrödinger and wave equations with BV coefficients." Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 33.6 (2016): 1473-1495.

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