TY - JOUR
T1 - Non-local Hamilton-Jacobi equations arising in dislocation dynamics
AU - Ishii, Hitoshi
AU - Matsumura, Yutaka
PY - 2010
Y1 - 2010
N2 - 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.
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.
KW - Dislocation dynamics
KW - Functional differential equations
KW - Hamilton-Jacobi equations
KW - Viscosity solutions
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U2 - 10.4171/ZAA/1411
DO - 10.4171/ZAA/1411
M3 - Article
AN - SCOPUS:77954221959
VL - 29
SP - 309
EP - 350
JO - Zeitschrift fur Analysis und ihre Anwendung
JF - Zeitschrift fur Analysis und ihre Anwendung
SN - 0232-2064
IS - 3
ER -