Non-local Hamilton-Jacobi equations arising in dislocation dynamics

Hitoshi Ishii; Yutaka Matsumura

doi:10.4171/ZAA/1411

Non-local Hamilton-Jacobi equations arising in dislocation dynamics

Hitoshi Ishii^*, Yutaka Matsumura

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	309-350
Number of pages	42
Journal	Zeitschrift fur Analysis und ihre Anwendung
Volume	29
Issue number	3
DOIs	https://doi.org/10.4171/ZAA/1411
Publication status	Published - 2010

Keywords

Dislocation dynamics
Functional differential equations
Hamilton-Jacobi equations
Viscosity solutions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.4171/ZAA/1411

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AB - 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.

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KW - Functional differential equations

KW - Hamilton-Jacobi equations

KW - Viscosity solutions

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Non-local Hamilton-Jacobi equations arising in dislocation dynamics

Abstract

Keywords

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