WEAK SOLUTIONS FOR DISLOCATION TYPE EQUATIONS

Abstract : We describe recent results obtained by G. Barles, P. Cardaliaguet, R. Monneau and the author recently. They are concerned with nonlocal Eikonal equations arising in the study of the dynamics of dislocation lines in crystals. These equations are nonlocal but also non monotone. We use a notion of weak solution to provide solutions for all time. Then, we discuss the link between these weak solutions and the classical viscosity solutions, and state some uniqueness results in particular cases. A counter-example to uniqueness is given.
Type de document :
Communication dans un congrès
Y. Giga, K. Ishii, S. Koike, T. Ozawa, N. Yamada. International Conference for the 25th Anniversary of Viscosity Solutions, Jun 2007, Tokyo, Japan. Gakkotosho Tokyo Japan, 30, pp.117-132, 2008, Gakuto International Series, Mathematical Sciences and Applications
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https://hal.archives-ouvertes.fr/hal-00243982
Contributeur : Olivier Ley <>
Soumis le : jeudi 7 février 2008 - 10:35:17
Dernière modification le : mercredi 12 juillet 2017 - 01:15:06
Document(s) archivé(s) le : lundi 10 mai 2010 - 13:27:40

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  • HAL Id : hal-00243982, version 1
  • ARXIV : 0802.0931

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Olivier Ley. WEAK SOLUTIONS FOR DISLOCATION TYPE EQUATIONS. Y. Giga, K. Ishii, S. Koike, T. Ozawa, N. Yamada. International Conference for the 25th Anniversary of Viscosity Solutions, Jun 2007, Tokyo, Japan. Gakkotosho Tokyo Japan, 30, pp.117-132, 2008, Gakuto International Series, Mathematical Sciences and Applications. <hal-00243982>

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