Academic Journal
Global existence for a system of non-linear and non-local transport equations describing the dynamics of dislocation densities
| العنوان: | Global existence for a system of non-linear and non-local transport equations describing the dynamics of dislocation densities |
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| المؤلفون: | Cannone, Marco, El Hajj, Ahmad, Monneau, Regis, Ribaud, Francis |
| المساهمون: | Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout (BEZOUT), Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO), Université d'Orléans (UO)-Centre National de la Recherche Scientifique (CNRS), Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS), Institut National de Recherche en Informatique et en Automatique (Inria)-École nationale des ponts et chaussées (ENPC) |
| المصدر: | ISSN: 0003-9527. |
| بيانات النشر: | CCSD Springer Verlag |
| سنة النشر: | 2010 |
| المجموعة: | Université d'Orléans: HAL |
| مصطلحات موضوعية: | dynamics of dislocation densities, Cauchy's problem, system of non-linear transport equations, system of non-local transport equations, system of hyperbolic equations, entropy, Riesz transform, Zygmund space, 54C70, 35L45, 35Q72, 74H20, 74H25, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] |
| الوصف: | International audience ; In this paper, we study the global in time existence problem for the Groma-Balogh model describing the dynamics of dislocation densities. This model is a two-dimensional model where the dislocation densities satisfy a system of transport equations such that the velocity vector field is the shear stress in the material, solving the equations of elasticity. This shear stress can be expressed as some Riesz transform of the dislocation densities. The main tool in the proof of this result is the existence of an entropy for this system |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/arxiv/0901.0219; ARXIV: 0901.0219 |
| DOI: | 10.1007/s00205-009-0235-8 |
| الاتاحة: | https://hal.science/hal-00319937 https://hal.science/hal-00319937v1/document https://hal.science/hal-00319937v1/file/exis_orlicz_simp2.pdf https://doi.org/10.1007/s00205-009-0235-8 |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.223EC2B7 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1007/s00205-009-0235-8 |
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