Well-Posedness Theory for a Nonconservative Burgers-Type System Arising in Dislocation Dynamics

DOI10.1137/060672170zbMath1149.35056OpenAlexW1972718589MaRDI QIDQ3506571

Ahmad El Hajj

Publication date: 16 June 2008

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/060672170

zbMATH Keywords

comparison principleone space dimensiondislocation densities in crystalssystem of nonlinear transport equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Initial value problems for first-order hyperbolic systems (35L45) Existence of solutions of dynamical problems in solid mechanics (74H20) Uniqueness of solutions of dynamical problems in solid mechanics (74H25)

Related Items (15)

Short time existence and uniqueness in Hölder spaces for the 2D dynamics of dislocation densities ⋮ 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 ⋮ Global existence results for eikonal equation with \(BV\) initial data ⋮ GLOBAL CONTINUOUS SOLUTIONS FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LARGE AND MONOTONE DATA ⋮ Global existence for a system of nonlinear and non-local transport equations describing the dynamics of dislocation densities ⋮ Existence and uniqueness of continuous solution for a non-local coupled system modeling the dynamics of dislocation densities ⋮ Convergence of an implicit scheme for diagonal non-conservative hyperbolic systems ⋮ Convergence and non-convergence of many-particle evolutions with multiple signs ⋮ Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities ⋮ Continuous solution for a non-linear eikonal system ⋮ Dynamics of Dislocation Densities in a Bounded Channel. Part II: Existence of Weak Solutions to a Singular Hamilton–Jacobi/Parabolic Strongly Coupled System ⋮ Global existence to a diagonal hyperbolic system for any BV initial data ⋮ UNIQUENESS RESULTS FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LARGE AND MONOTONE DATA

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