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WELL-POSEDNESS OF HAMILTON-JACOBI EQUATIONS WITH CAPUTO'S TIME-FRACTIONAL DERIVATIVE

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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
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

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