Non-isothermal, non-Newtonian Hele-Shaw flows within Cattaneo's heat flux law

Authors:
Ming Fang;Robert P. Gilbert
Affiliations:
Department of Mathematics, Norfolk State University, Norfolk, VA 23504, USA;Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2007

Citing 3
Cited 0

Blow-up estimates for a nonlinear hyperbolic heat equation

SIAM Journal on Mathematical Analysis
Nonisothermal, nonNewtonian Hele-Shaw flows, part II: asymptotics and existence of weak solutions

Nonlinear Analysis: Theory, Methods & Applications
Nonlinear systems arising from nonisothermal, non-Newtonian Hele-Shaw flows in the presence of body forces and sources

Mathematical and Computer Modelling: An International Journal

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Abstract

In this paper, we consider a non-isothermal, non-Newtonian injection process. This leads to the study of a novel elliptic-hyperbolic system. The hyperbolic nature of the system arises because we replace the infinite speed of propagation from classical, thermal elasticity by a finite propagation velocity. We present a formal derivation of the elliptic-hyperbolic system starting from conservations of mass, momentum, and energy in a three-dimensional domain, where the removal of the infinite propagation speed is achieved using Cattaneo's law for heat conduction. The existence of weak solutions to certain elliptic-hyperbolic problems associated with the resulting equations is proved.