We investigate a class of non-local Hamilton–Jacobi equations arising in dislocation dynamics. The class of Hamilton–Jacobi equations treated here is a variation of those studied by N. Forcadel, C. Imbert and R. Monneau in [Discrete Contin. Dyn. Syst. 23 (2009)(3), 785 – 826], and the new feature lies in the singularity at the origin of the kernel functions which describe non-local eﬀects. For the class of Hamilton–Jacobi equations, we establish some stability properties of (viscosity) solutions, comparison theorems between subsolutions and supersolutions and existence theorems of solutions.
Cite this article
Hitoshi Ishii, Yutaka Matsumura, Non-Local Hamilton-Jacobi Equations Arising in Dislocation Dynamics. Z. Anal. Anwend. 29 (2010), no. 3, pp. 309–350