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On a dynamic boundary condition for singular degenerate parabolic equations in a half space

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Title: On a dynamic boundary condition for singular degenerate parabolic equations in a half space
Authors: Giga, Yoshikazu Browse this author
Hamamuki, Nao Browse this author
Keywords: dynamic boundary condition
geometric equations
comparison principle
viscosity solutions
Issue Date: 28-Apr-2018
Publisher: Department of Mathematics, Hokkaido University
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1110
Start Page: 1
End Page: 38
Abstract: We consider the initial value problem for a fully-nonlinear degenerate parabolic equation with a dynamic boundary condition in a half space. Our setting includes geometric equations with singularity such as the level-set mean curvature flow equation. We establish a comparison principle for a viscosity sub- and supersolution. We also prove existence of solutions and Lipschitz regularity of the unique solution. Moreover, relation to other types of boundary conditions is investigated by studying the asymptotic behavior of the solution with respect to a coefficient of the dynamic boundary condition.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/70072
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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