LEADER 03460nam 2200637 450 001 996466639003316 005 20220426205609.0 010 $a1-280-86504-0 010 $a9786610865048 010 $a3-540-72187-8 024 7 $a10.1007/978-3-540-72187-1 035 $a(CKB)1000000000282821 035 $a(EBL)3036681 035 $a(SSID)ssj0000299186 035 $a(PQKBManifestationID)11237666 035 $a(PQKBTitleCode)TC0000299186 035 $a(PQKBWorkID)10257282 035 $a(PQKB)10725716 035 $a(DE-He213)978-3-540-72187-1 035 $a(MiAaPQ)EBC3036681 035 $a(MiAaPQ)EBC6698645 035 $a(Au-PeEL)EBL6698645 035 $a(PPN)123161940 035 $a(EXLCZ)991000000000282821 100 $a20220426d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aHyperbolic systems of balance laws $electures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003 /$fedited by Alberto Bressan [and three others] 205 $a1st ed. 2007. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer,$d[2007] 210 4$dİ2007 215 $a1 online resource (364 p.) 225 1 $aC.I.M.E. Foundation Subseries ;$v1911 300 $aDescription based upon print version of record. 311 $a3-540-72186-X 320 $aIncludes bibliographical references. 327 $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. 330 $aThe present Cime volume includes four lectures by Bressan, Serre, Zumbrun and Williams and an appendix with a Tutorial on Center Manifold Theorem by Bressan. Bressan?s notes start with an extensive review of the theory of hyperbolic conservation laws. Then he introduces the vanishing viscosity approach and explains clearly the building blocks of the theory in particular the crucial role of the decomposition by travelling waves. Serre focuses on existence and stability for discrete shock profiles, he reviews the existence both in the rational and in the irrational cases and gives a concise introduction to the use of spectral methods for stability analysis. Finally the lectures by Williams and Zumbrun deal with the stability of multidimensional fronts. Williams? lecture describes the stability of multidimensional viscous shocks: the small viscosity limit, linearization and conjugation, Evans functions, Lopatinski determinants etc. Zumbrun discusses planar stability for viscous shocks with a realistic physical viscosity, necessary and sufficient conditions for nonlinear stability, in analogy to the Lopatinski condition obtained by Majda for the inviscid case. 410 0$aC.I.M.E. Foundation Subseries ;$v1911 606 $aShock waves$xMathematics$vCongresses 606 $aDifferential equations, Hyperbolic$vCongresses 615 0$aShock waves$xMathematics 615 0$aDifferential equations, Hyperbolic 676 $a515/.353 702 $aBressan$b Alberto$f1956- 712 02$aCentro internazionale matematico estivo. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466639003316 996 $aHyperbolic systems of balance laws$9230584 997 $aUNISA