Nonlinear degenerate parabolic equations for a thermohydraulic model

Takesi Fukao; Masahiro Kubo

doi:10.3934/proc.2007.2007.399

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2007, Volume 2007: 399-408. Doi: 10.3934/proc.2007.2007.399 open access

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Nonlinear degenerate parabolic equations for a thermohydraulic model

Takesi Fukao^1, and
Masahiro Kubo^2,

1.
General Education, Gifu Natioinal College of Technology, Kamimakuwa 2236-2, Motosu-shi, Gifu 501-0495
2.
Department of Mathematics, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555

Received: August 31, 2006

Revised: April 30, 2007

Published: August 2007

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Abstract

In this paper, we consider an initial boundary value problem for a system of second order partial differential equations. This system consists of the Navier-Stokes equations and a nonlinear heat equation. More precisely, we impose a nonlinear heat flux associated with a class of maximal monotone graphs with a Neumann boundary condition. We establish the conditions required to prove the existence of a solution for the given data.

Keywords:

Degenerate parabolic equation,
Navier-Stokes equations.

Mathematics Subject Classification: Primary: 35K65, 76D05; Secondary: 35G30.

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