Formal derivation and existence result of an approximate model on dislocation densities
DOI10.1002/zamm.201700038zbMath1529.35282OpenAlexW2791588980MaRDI QIDQ6086210
Zaynab Salloum, Vivian Rizik, Hassan Ibrahim
Publication date: 12 December 2023
Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/zamm.201700038
Crystalline structure (74E15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Singular parabolic equations (35K67) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Comparison principles in context of PDEs (35B51) Initial-boundary value problems for second-order parabolic systems (35K51)
Cites Work
- Dislocation dynamics: from microscopic models to macroscopic crystal plasticity
- Dynamics of dislocation densities in a bounded channel. I: Smooth solutions to a singular coupled parabolic system
- Global existence for a system of nonlinear and non-local transport equations describing the dynamics of dislocation densities
- Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities
- A transport formulation for moving fronts and application to dislocation dynamics
- Well-Posedness Theory for a Nonconservative Burgers-Type System Arising in Dislocation Dynamics
- Dynamics of Dislocation Densities in a Bounded Channel. Part II: Existence of Weak Solutions to a Singular Hamilton–Jacobi/Parabolic Strongly Coupled System
- Derivation and study of dynamical models of dislocation densities
- A convergent scheme for a non-local coupled system modelling dislocations densities dynamics
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