On a Hele–Shaw Type Domain Evolution with Convected Surface Energy Density: The Third‐Order Problem

Autor:	G Georg Prokert, Matthias Günther
Přispěvatelé:	Center for Analysis, Scientific Computing & Appl., Applied Analysis
Rok vydání:	2006
Předmět:	Sobolev space Surface tension Computational Mathematics Flow (mathematics) Applied Mathematics Operator (physics) Boundary problem Mathematical analysis Boundary (topology) Bilinear form Balanced flow Analysis Mathematics
Zdroj:	SIAM Journal on Mathematical Analysis, 38(4), 1154-1185. Society for Industrial and Applied Mathematics (SIAM)
ISSN:	1095-7154 0036-1410
Popis:	We investigate a moving boundary problem with a gradient flow structure which generalizes Hele–Shaw flow driven solely by surface tension to the case of nonconstant surface tension coefficient taken along with the liquid particles at boundary. The resulting evolution problem is first order in time, contains a third-order nonlinear pseudodifferential operator and is degenerate parabolic. Well-posedness of this problem in Sobolev scales is proved. The main tool is the construction of a variable symmetric bilinear form so that the third-order operator is semibounded with respect to it. Moreover, we show global existence and convergence to an equilibrium for solutions near trivial equilibria (balls with constant surface tension coefficient). Finally, numerical examples in 2D and 3D are given.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::be22fdb214442d121842b9a5da00c562 https://doi.org/10.1137/050626995 Zobrazit plný text záznamu Plný text ve formátu PDF