Existence and Uniqueness of Continuous Solution for a Non-local Coupled System Modeling the Dynamics of Dislocation Densities
| Autor: | Aya Oussaily, A. El Hajj |
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| Rok vydání: | 2021 |
| Předmět: |
Applied Mathematics
Mathematical analysis General Engineering Space (mathematics) 01 natural sciences 010305 fluids & plasmas Term (time) 010101 applied mathematics Entropy (classical thermodynamics) Viscosity Modeling and Simulation 0103 physical sciences Uniqueness Limit (mathematics) 0101 mathematics Dislocation Viscosity solution Mathematics |
| Zdroj: | Journal of Nonlinear Science. 31 |
| ISSN: | 1432-1467 0938-8974 |
| Popis: | In this paper, we study a non-local coupled system that arises in the theory of dislocations densities dynamics. Based on a new gradient entropy estimate in $$L \log L$$ space, we prove the global existence of a continuous solution. The approach is made by adding a viscosity term and passing to the limit for vanishing viscosity. A comparison principle with respect to time is used for proving uniqueness of the solution for the local problem. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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