Nonlinear degenerate parabolic equations for a thermohydraulic model

Pages: 399 - 408, Issue Special, September 2007

 Abstract        Full Text (220.3K)              

Takesi Fukao - General Education, Gifu Natioinal College of Technology, Kamimakuwa 2236-2, Motosu-shi, Gifu 501-0495, Japan (email)
Masahiro Kubo - Department of Mathematics, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan (email)

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.

Received: September 2006;      Revised: May 2007;      Published: September 2007.