2023-03-22T18:32:33Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/699022022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116WELL-POSEDNESS OF HAMILTON-JACOBI EQUATIONS WITH CAPUTO'S TIME-FRACTIONAL DERIVATIVEGIGA, YOSHIKAZUNamba, Tokinagaopen access410A 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.Department of Mathematics, Hokkaido University2016-12-19engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84242http://hdl.handle.net/2115/6990210.14943/84242Hokkaido University Preprint Series in Mathematics1098131https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69902/1/pre1098.pdfapplication/pdf196.08 KB2016-12-19