Existence of viscosity solution for a singular Hamilton–Jacobi equation

Abstract

In this paper we study the existence of a singular Hamilton–Jacobi equation under the framework of viscosity solutions. The analysis is inspired by the arguments of [8] where a study of a model on dislocation dynamics was considered.

Keywords

• Hamilton–Jacobi equations
• Scalar conservation laws
• Viscosity solutions
• Entropy solutions
• Dynamics of dislocation densities