Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 52, No. 3, pp. 343-355 (1995)

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A Wave Equation with a Dirac Distribution

Yvan Martel

Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie,
4, place Jussieu, 75252 Paris Cedex 05 - FRANCE

Abstract: The sine-Gordon equation including a Dirac distribution: $u_{tt}-u_{xx}+\sin u=\delta_a\sin u$ models the interaction between a soliton and a local impurity occuring during transmission through disordered media. Here, we study the Cauchy problem for this equation and we show the existence and uniqueness of a solution in the energy space.

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Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.

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