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Diagonal hyperbolic systems with large and monotone data Part I: Global continuous solutions

Abstract : In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and non-decreasing initial data. We remark that these results cover the case of systems which are hyperbolic but not strictly hyperbolic. Physically, this kind of diagonal hyperbolic systems appears naturally in the modelling of the dynamics of dislocation densities.
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https://hal.archives-ouvertes.fr/hal-00375045
Contributor : Ahmad El Hajj <>
Submitted on : Saturday, April 11, 2009 - 7:24:29 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Thursday, June 10, 2010 - 8:23:22 PM

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Ahmad El Hajj, Régis Monneau. Diagonal hyperbolic systems with large and monotone data Part I: Global continuous solutions. Journal of Hyperbolic Differential Equations, World Scientific Publishing, 2010, 7 (1), pp.1-26. ⟨10.1142/S0219891610002050⟩. ⟨hal-00375045⟩

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