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Nonlocal spatially inhomogeneous Hamilton-Jacobi equation with unusual free boundary

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84081

Title: Nonlocal spatially inhomogeneous Hamilton-Jacobi equation with unusual free boundary
Authors: Giga, Yoshikazu Browse this author
Gorka, Przemyslaw Browse this author
Rybka, Piotr Browse this author
Keywords: driven curvature flow
singular energies
Hamilton-Jacobi equation
free oundary
discontinuous Hamiltonian
comparison principle
Issue Date: 2-Feb-2009
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 933
Start Page: 1
End Page: 27
Abstract: We 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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69741
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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