|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
WELL-POSEDNESS OF HAMILTON-JACOBI EQUATIONS WITH CAPUTO'S TIME-FRACTIONAL DERIVATIVE
| Title: | WELL-POSEDNESS OF HAMILTON-JACOBI EQUATIONS WITH CAPUTO'S TIME-FRACTIONAL DERIVATIVE |
| Authors: | GIGA, YOSHIKAZU Browse this author | | Namba, Tokinaga Browse this author |
| Issue Date: | 19-Dec-2016 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1098 |
| Start Page: | 1 |
| End Page: | 31 |
| Abstract: | A Hamilton-Jacobi equation with Caputo's time-fractional deriv- ative of order less than one is considered. The notion of a viscosity solution is introduced to prove unique existence of a solution to the initial value problem under periodic boundary conditions. For this purpose comparison principle as well as Perron's method is established. Stability with respect to the order of derivative as well as the standard one is studied. Regularity of a solution is also discussed. Our results in particular apply to a linear transport equation with time-fractional derivatives with variable coefficients. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69902 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
|
Submitter: 数学紀要登録作業用
|
