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020 _a9783540721871
_9978-3-540-72187-1
024 7 _a10.1007/978-3-540-72187-1
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.353
_223
100 1 _aBressan, Alberto.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aHyperbolic Systems of Balance Laws
_h[electronic resource] :
_bLectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14–21, 2003 /
_cby Alberto Bressan, Denis Serre, Mark Williams, Kevin Zumbrun ; edited by Pierangelo Marcati.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2007.
300 _aXII, 356 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aC.I.M.E. Foundation Subseries ;
_v1911
505 0 _aBV Solutions to Hyperbolic Systems by Vanishing Viscosity -- Discrete Shock Profiles: Existence and Stability -- Stability of Multidimensional Viscous Shocks -- Planar Stability Criteria for Viscous Shock Waves of Systems with Real Viscosity.
520 _aThe present Cime volume includes four lectures by Bressan, Serre, Zumbrun and Williams and an appendix with a Tutorial on Center Manifold Theorem by Bressan. Bressan’s notes start with an extensive review of the theory of hyperbolic conservation laws. Then he introduces the vanishing viscosity approach and explains clearly the building blocks of the theory in particular the crucial role of the decomposition by travelling waves. Serre focuses on existence and stability for discrete shock profiles, he reviews the existence both in the rational and in the irrational cases and gives a concise introduction to the use of spectral methods for stability analysis. Finally the lectures by Williams and Zumbrun deal with the stability of multidimensional fronts. Williams’ lecture describes the stability of multidimensional viscous shocks: the small viscosity limit, linearization and conjugation, Evans functions, Lopatinski determinants etc. Zumbrun discusses planar stability for viscous shocks with a realistic physical viscosity, necessary and sufficient conditions for nonlinear stability, in analogy to the Lopatinski condition obtained by Majda for the inviscid case.
650 0 _aDifferential equations, partial.
650 0 _aNumerical analysis.
650 1 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aClassical and Continuum Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P2100X
650 2 4 _aNumerical Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M14050
700 1 _aSerre, Denis.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aWilliams, Mark.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aZumbrun, Kevin.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aMarcati, Pierangelo.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540837770
776 0 8 _iPrinted edition:
_z9783540721864
830 0 _aC.I.M.E. Foundation Subseries ;
_v1911
856 4 0 _uhttps://doi.org/10.1007/978-3-540-72187-1
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10312
_d10312