2024-03-28T20:33:39Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/697412022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Nonlocal spatially inhomogeneous Hamilton-Jacobi equation with unusual free boundaryGiga, YoshikazuGorka, PrzemyslawRybka, Piotropen accessdriven curvature flowsingular energiesHamilton-Jacobi equationfree oundarydiscontinuous Hamiltoniancomparison principle410We consider the weighted mean curvature flow with a driving term in the plane. For nisotropy functions this evolution problem degenerates to a first order Hamilton-Jacobi quation with a free boundary. The resulting problem may be written as a Hamilton-Jacobi quation with a spatially non-local and discontinuous Hamiltonian. We prove existence nd uniqueness of solutions. On the way we show a comparison principle and a stability heorem for viscosity solutions.Department of Mathematics, Hokkaido University2009-02-02engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84081http://hdl.handle.net/2115/6974110.14943/84081Hokkaido University Preprint Series in Mathematics933127https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69741/1/pre933.pdfapplication/pdf216.55 KB2009-02-02