Systems of partial differential equations of mixed hyperbolic–parabolic type

We prove the global existence and uniqueness of solutions of certain mixed hyperbolic–parabolic systems of partial differential equations in one space dimension with initial data that is assumed to be pointwise bounded with possibly large oscillation and with small total energy. The systems we consi...

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Bibliographic Details
Published in:Journal of Differential Equations Vol. 204; no. 1; pp. 163 - 201
Main Authors: Tsyganov, Eugene, Hoff, David
Format: Journal Article
Language:English
Published: Elsevier Inc 10.09.2004
Subjects:
Compressible magnetohydrodynamics
Compressible Navier–Stokes equations
Systems of mixed hyperbolic–parabolic type
35A05
Compressible magnetohydrodynamics
Compressible Navier–Stokes equations
35M10
76W05
76N10
Systems of mixed hyperbolic–parabolic type
ISSN:0022-0396, 1090-2732
Online Access:Get full text
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Summary:We prove the global existence and uniqueness of solutions of certain mixed hyperbolic–parabolic systems of partial differential equations in one space dimension with initial data that is assumed to be pointwise bounded with possibly large oscillation and with small total energy. The systems we consider are general enough to include the Navier–Stokes equations of compressible flow, the equations of compressible MHD, models of chemical combustion, and others. In particular, the application of our results to the MHD system gives an existence result which is new.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2004.03.010