Hyperbolic Conservation Laws In Continuum Physics / Edition 2

Hyperbolic Conservation Laws In Continuum Physics / Edition 2

by Constantine M. Dafermos
     
 

ISBN-10: 3540254528

ISBN-13: 9783540254522

Pub. Date: 03/08/2008

Publisher: Springer-Verlag New York, LLC

This masterly exposition of the mathematical theory of hyperbolic system laws brings out the intimate connection with continuum thermodynamics, emphasizing issues in which the analysis may reveal something about the physics and, in return, the underlying physical structure may direct and drive the analysis. The reader should have a certain mathematical

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Overview

This masterly exposition of the mathematical theory of hyperbolic system laws brings out the intimate connection with continuum thermodynamics, emphasizing issues in which the analysis may reveal something about the physics and, in return, the underlying physical structure may direct and drive the analysis. The reader should have a certain mathematical sophistication and be familiar with the rudiments of the qualitative theory of partial differential equations, whereas the required notions from continuum physics are introduced from scratch.

The 2nd edition contains a new chapter recounting the exciting recent developments on the vanishing viscosity method; numerous new sections have been incorporated in preexisting chapters, to introduce newly derived results or present older material, omitted in the 1st edition. In addition, a substantial portion of the original text has been reorganized so as to streamline the exposition, enrich the collection of examples and improve the notation. The bibliography has been updated and expanded, now comprising over one thousand titles.

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Product Details

ISBN-13:
9783540254522
Publisher:
Springer-Verlag New York, LLC
Publication date:
03/08/2008
Series:
Grundlehren der mathematischen Wissenschaften Series, #325
Edition description:
REV
Pages:
652
Product dimensions:
1.44(w) x 6.14(h) x 9.21(d)

Table of Contents

IBalance laws1
IIIntroduction to continuum physics25
IIIHyperbolic systems of balance laws51
IVThe Cauchy problem67
VEntropy and the stability of classical solutions87
VIThe L[superscript 1] theory for Scalar conservation laws123
VIIHyperbolic systems of balance laws in one-space dimension173
VIIIAdmissible shocks205
IXAdmissible wave fans and the Riemann problem239
XGeneralized characteristics295
XIGenuinely nonlinear Scalar conservation laws301
XIIGenuinely nonlinear systems of two conservation laws343
XIIIThe random choice method405
XIVThe front tracking method and standard Riemann semigroups443
XVConstruction of BV solutions by the vanishing viscosity method483
XVICompensated compactness511

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