کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9501706 | 1338778 | 2005 | 29 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A non-local regularization of first order Hamilton-Jacobi equations
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In this paper, we investigate the regularizing effect of a non-local operator on first-order Hamilton-Jacobi equations. We prove that there exists a unique solution that is C2 in space and C1 in time. In order to do so, we combine viscosity solution techniques and Green's function techniques. Viscosity solution theory provides the existence of a W1,â solution as well as uniqueness and stability results. A Duhamel's integral representation of the equation involving the Green's function permits to prove further regularity. We also state the existence of Câ solutions (in space and time) under suitable assumptions on the Hamiltonian. We finally give an error estimate in Lâ norm between the viscosity solution of the pure Hamilton-Jacobi equation and the solution of the integro-differential equation with a vanishing non-local part.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 211, Issue 1, 1 April 2005, Pages 218-246
Journal: Journal of Differential Equations - Volume 211, Issue 1, 1 April 2005, Pages 218-246
نویسندگان
Cyril Imbert,