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:https://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
Publisher:	Department of Mathematics, Hokkaido University
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

OAI-PMH ( junii2 , jpcoar_1.0 )

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