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

GIGA, YOSHIKAZU; Namba, Tokinaga

Hokkaido University Preprint Series in Mathematics, 2016, 1098, 1-31

Permalink : https://doi.org/10.14943/84242

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DOI	https://doi.org/10.14943/84242
URI	https://hdl.handle.net/2115/69902
タイトル	WELL-POSEDNESS OF HAMILTON-JACOBI EQUATIONS WITH CAPUTO'S TIME-FRACTIONAL DERIVATIVE
著者	著者名 GIGA, YOSHIKAZU
著者	著者名 Namba, Tokinaga
言語	英語
発行日	2016-12-19
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	1098
ページ	1-31
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record