Time-dependent obstacle problem in thermohydraulics

Takeshi Fukao; Masahiro Kubo

doi:10.3934/proc.2009.2009.240

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2009, Volume 2009: 240-249. Doi: 10.3934/proc.2009.2009.240 open access

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Time-dependent obstacle problem in thermohydraulics

Takeshi Fukao^1, and
Masahiro Kubo^2,

1.
Department of Mathematics, Kyoto University of Education, Fuji 1, Fukakusa Fushimi-ku, Kyoto 612-8522
2.
Department of Mathematics, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555

Received: June 30, 2008

Revised: January 31, 2009

Published: August 2009

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Abstract

Obstacle problems, mathematical models of some nonlinear phenomena accompanying a free boundary, have been well studied. In this paper, the existence and uniqueness of a system between the obstacle problem and the Navier-Stokes equations is considered. The abstract theory for evolution equations governed by a subdifferential of the indicator functional on a time-dependent, closed, and convex set is applied to show the main theorem. $L^\infty $-estimate is an important lemma to prove the existence theorem.

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Mathematics Subject Classification: Primary: 35K65, 76D05; Secondary: 35G3.

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