Existence of viscosity solution for a singular Hamilton-Jacobi equation

DOI10.1016/j.ajmsc.2014.03.001zbMath1308.70030OpenAlexW2002237042MaRDI QIDQ486124

Yong-Cai Geng, Sumit K. Garg

Publication date: 14 January 2015

Published in: Arab Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ajmsc.2014.03.001

zbMATH Keywords

Hamilton-Jacobi equationsentropy solutionsviscosity solutionsscalar conservation lawsdynamics of dislocation densities

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Entropy in general topology (54C70) Hamilton-Jacobi equations in mechanics (70H20) 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)

Cites Work

• Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities
• Viscosity solutions of Hamilton-Jacobi equations
• A note on front tracking and the equivalence between viscosity solutions of Hamilton-Jacobi equations and entropy solutions of scalar conservation laws
• Solutions of Hamilton-Jacobi equations and scalar conservation laws with discontinuous space-time dependence
• Existence and uniqueness of the entropy solution to a nonlinear hyperbolic equation
• On existence and uniqueness of solutions of Hamilton-Jacobi equations
• Scalar conservation laws and Hamilton-Jacobi equations in one-space variable
• Numerical Schemes for Conservation Laws via Hamilton-Jacobi Equations
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