Non-Local Hamilton-Jacobi Equations Arising in Dislocation Dynamics

  • Hitoshi Ishii

    Waseda University, Tokyo, Japan
  • Yutaka Matsumura

    Waseda University, Tokyo, Japan


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

DOI 10.4171/ZAA/1411