GLOBAL CONTINUOUS SOLUTIONS FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LARGE AND MONOTONE DATA

DOI10.1142/S0219891610002050zbMath1198.35143arXiv0804.4137MaRDI QIDQ3560074

Ahmad El Hajj, Régis Monneau

Publication date: 19 May 2010

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.4137

zbMATH Keywords

Burgers equationdynamics of dislocation densitiesnonlinear transport equationsgradient entropy estimate

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) First-order nonlinear hyperbolic equations (35L60) Initial value problems for first-order hyperbolic systems (35L45) Uniqueness of solutions of dynamical problems in solid mechanics (74H25)

Related Items (10)

Global \(BV\) solution for a non-local coupled system modeling the dynamics of dislocation densities ⋮ Entropy solutions to a non-conservative and non-strictly hyperbolic diagonal system inspired by dislocation dynamics ⋮ Global solution for a non-local eikonal equation modelling dislocation dynamics ⋮ Existence and uniqueness of continuous solution for a non-local coupled system modeling the dynamics of dislocation densities ⋮ \(BV\) solution for a non-linear Hamilton-Jacobi system ⋮ Continuous solution for a non-linear eikonal system ⋮ A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data ⋮ Global existence to a diagonal hyperbolic system for any BV initial data ⋮ UNIQUENESS RESULTS FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LARGE AND MONOTONE DATA ⋮ Convergent semi-explicit scheme to a non-linear eikonal system

Cites Work

• Unnamed Item
• Unnamed Item
• Transport equation and Cauchy problem for BV vector fields
• Ordinary differential equations, transport theory and Sobolev spaces
• Convergence of approximate solutions to conservation laws
• Compact sets in the space \(L^ p(0,T;B)\)
• Multiple slip in a strain-gradient plasticity model motivated by a statistical-mechanics description of dislocations
• Vanishing viscosity solutions of nonlinear hyperbolic systems
• Well-Posedness Theory for a Nonconservative Burgers-Type System Arising in Dislocation Dynamics
• GRAPH SOLUTIONS OF NONLINEAR HYPERBOLIC SYSTEMS
• Discontinuous solutions of non-linear differential equations
• A convergent scheme for a non-local coupled system modelling dislocations densities dynamics
• Solutions in the large for nonlinear hyperbolic systems of equations
• Global smooth solutions of some quasilinear hyperbolic systems with large data

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