000 04082nam a22004935i 4500
001 978-3-540-29089-6
003 DE-He213
005 20161121230934.0
007 cr nn 008mamaa
008 100301s2005 gw | s |||| 0|eng d
020 _a9783540290896
_9978-3-540-29089-6
024 7 _a10.1007/3-540-29089-3
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aDafermos, Constantine M.
_eauthor.
245 1 0 _aHyberbolic Conservation Laws in Continuum Physics
_h[electronic resource] /
_cby Constantine M. Dafermos.
250 _aSecond Edition.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2005.
300 _aXX, 626 p. 39 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v325
505 0 _aBalance Laws -- to Continuum Physics -- Hyperbolic Systems of Balance Laws -- The Cauchy Problem -- Entropy and the Stability of Classical Solutions -- The L1 Theory for Scalar Conservation Laws -- Hyperbolic Systems of Balance Laws in One-Space Dimension -- Admissible Shocks -- Admissible Wave Fans and the Riemann Problem -- Generalized Characteristics. -- Genuinely Nonlinear Scalar Conservation Laws -- Genuinely Nonlinear Systems of Two Conservation Laws -- The Random Choice Method -- The Front Tracking Method and Standard Riemann Semigroups -- Construction of BV Solutions by the Vanishing Viscosity Method -- Compensated Compactness.
520 _aThis masterly exposition of the mathematical theory of hyperbolic system for conservation laws brings out the intimate connection with continuum thermodynamics, by emphasising 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 is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of the qualitative theory of partial differential equations, whereas the required notions from continuum physics are introduced from scratch. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics who may need analytical tools; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conservation laws. 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 first edition, whose relevance and importance has been underscored by current trends in research. In addition, a substantal portion of the original text has been revamped so as to streamline the exposition, enrich the collection of examples and improve the notation. The bibliography has been updated and expanded as well, now comprising over one thousand titles. .
650 0 _aMathematics.
650 0 _aPartial differential equations.
650 0 _aMechanics.
650 0 _aThermodynamics.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aThermodynamics.
650 2 4 _aMechanics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540254522
830 0 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v325
856 4 0 _uhttp://dx.doi.org/10.1007/3-540-29089-3
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c506170
_d506170