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

Giga, Yoshikazu; Hamamuki, Nao

Hokkaido University Preprint Series in Mathematics, 2018, 1110, 1-38

Permalink : https://doi.org/10.14943/84298

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アクセス権	open access
DOI	https://doi.org/10.14943/84298
URI	https://hdl.handle.net/2115/70072
タイトル	On a dynamic boundary condition for singular degenerate parabolic equations in a half space
著者	著者名 Giga, Yoshikazu
著者	著者名 Hamamuki, Nao
言語	英語
キーワード	dynamic boundary condition
	geometric equations
	comparison principle
	viscosity solutions
発行日	2018-04-28
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	1110
ページ	1-38
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record