Existence and uniqueness of continuous solution for a non-local coupled system modeling the dynamics of dislocation densities

DOI10.1007/S00332-021-09676-7zbMATH Open1462.35332OpenAlexW3124754695MaRDI QIDQ2022639

A. Oussaily, Ahmad El Hajj

Publication date: 29 April 2021

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00332-021-09676-7

zbMATH Keywords

viscosity solutiondislocation dynamicsentropy estimateHamilton-Jacobi systemnon-local eikonal systemnon-local transport system

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for first-order hyperbolic systems (35L45) Initial value problems for nonlinear first-order PDEs (35F25) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Existence of solutions of dynamical problems in solid mechanics (74H20) Uniqueness of solutions of dynamical problems in solid mechanics (74H25) First-order hyperbolic systems (35L40) Hamilton-Jacobi equations (35F21) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Related Items (15)

Title not available (Why is that?) ⋮ Title not available (Why is that?) ⋮ Existence and uniqueness of bounded stable solutions to the Peierls-Nabarro model for curved dislocations ⋮ Global \(BV\) solution for a non-local coupled system modeling the dynamics of dislocation densities ⋮ Formal derivation and existence result of an approximate model on dislocation densities ⋮ Entropy solutions to a non-conservative and non-strictly hyperbolic diagonal system inspired by dislocation dynamics ⋮ Long time behavior of dynamic solution to Peierls-Nabarro dislocation model ⋮ A convergent scheme for a nonlocal Hamilton Jacobi equation modelling dislocation dynamics ⋮ A convergent scheme for a non-local coupled system modelling dislocations densities dynamics ⋮ Global Existence Results and Uniqueness for Dislocation Equations ⋮ Convergent scheme for a non-local transport system modeling dislocations dynamics ⋮ Convergence of an implicit scheme for diagonal non-conservative hyperbolic systems ⋮ Existence and uniqueness results to a system of Hamilton-Jacobi equations with application to dislocation dynamics ⋮ Time-homogenization of a first order system arising in the modelling of the dynamics of dislocation densities ⋮ Continuous solution for a non-linear eikonal system

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