Dynamics of Dislocation Densities in a Bounded Channel. Part II: Existence of Weak Solutions to a Singular Hamilton–Jacobi/Parabolic Strongly Coupled System

DOI10.1080/03605300903011861zbMath1175.70020arXiv0903.1435OpenAlexW1978974498MaRDI QIDQ3643217

Mustapha Jazar, Régis Monneau, Hassan Ibrahim

Publication date: 10 November 2009

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.1435

zbMATH Keywords

entropyHamilton-Jacobi equationsOrlicz spacesparabolic equationsviscosity solutions

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Entropy in general topology (54C70) Hamilton-Jacobi equations in mechanics (70H20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (5)

On a parabolic logarithmic Sobolev inequality ⋮ 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 ⋮ Global existence of solutions to a singular parabolic/Hamilton-Jacobi coupled system with Dirichlet conditions ⋮ Homogenization of accelerated Frenkel-Kontorova models with $n$ types of particles

Cites Work

• Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities
• Mean value properties of solutions to parabolic equations with variable coefficients
• Asymptotic behaviour of fundamental solutions and potential theory of parabolic operators with variable coefficients
• Viscosity solutions of Hamilton-Jacobi equations
• Well-Posedness Theory for a Nonconservative Burgers-Type System Arising in Dislocation Dynamics
• A convergent scheme for a non-local coupled system modelling dislocations densities dynamics
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