LEADER 01702nam 2200409 n 450 001 996390452403316 005 20200824120429.0 035 $a(CKB)4940000000100903 035 $a(EEBO)2240864518 035 $a(UnM)99835929e 035 $a(UnM)99835929 035 $a(EXLCZ)994940000000100903 100 $a19900817d1594 uy | 101 0 $aeng 135 $aurbn||||a|bb| 200 00$aSymbolęography$b[electronic resource] $ewhich may be termed the art, description, or image of instruments. Or the paterne of pręsidents. Or the notarie or scriuener. The first part of instruments extraiudiciall, the third time corrected by William West of the Inner Temple Esquire, first author thereof 210 $aImprinted at London $cIn Fleetstreat, by Charles Yetsweirt Esq. and are to be sold at his house within Temple Barre, neere to the Middle Temple gate$dAnno Do. 1594 215 $a[622] p 300 $aAt foot of title: Cum priuilegio Regię Maiestatis. 300 $aSignatures: [fleuron]? A-2P¹? (-2P10). 300 $aReproduction of the original in the Cambridge University Library. 330 $aeebo-0021 606 $aConveyancing$zGreat Britain$vEarly works to 1800 606 $aEquity pleading and procedure$zGreat Britain$vEarly works to 1800 606 $aForms (Law)$zGreat Britain$vEarly works to 1800 615 0$aConveyancing 615 0$aEquity pleading and procedure 615 0$aForms (Law) 700 $aWest$b William$ffl. 1568-1594.$01001542 801 0$bCu-RivES 801 1$bCu-RivES 801 2$bCStRLIN 801 2$bWaOLN 906 $aBOOK 912 $a996390452403316 996 $aSymbolęography$92303096 997 $aUNISA LEADER 01024nam0-22002891i-450 001 990005064100403321 005 20230707112313.0 035 $a000506410 035 $aFED01000506410 035 $a(Aleph)000506410FED01 100 $a19990604g19549999km-y0itay50------ba 101 0 $aita 105 $af-------001yy 200 1 $aAntologia del grande attore$eraccolta di memorie e di saggi dei grandi attori italiani dalla riforma goldoniana ad oggi, preceduti da scritti critici dei maggiori studiosi dell'epoca e da una introduzione storica$fVito Pandolfi 210 $aBari$cLaterza$d1954 215 $a533 p., [30] tav.$d25 cm 225 1 $aBiblioteca dello spettacolo$v2 676 $a792.028$v22$zita 700 1$aPandolfi,$bVito$f<1917-1974>$0156903 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990005064100403321 952 $aDE 701$bFil.Mod. 4402$fFLFBC 952 $a792.02 PAN 1$bIst.f.m.4402$fFLFBC 959 $aFLFBC 996 $aAntologia del grande attore$9532149 997 $aUNINA LEADER 06406nam 2200685 450 001 996466386703316 005 20231110232035.0 010 $a3-030-83785-8 035 $a(CKB)4950000000280582 035 $a(MiAaPQ)EBC6788039 035 $a(Au-PeEL)EBL6788039 035 $a(OCoLC)1280276014 035 $a(PPN)258295961 035 $a(EXLCZ)994950000000280582 100 $a20220712d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConvex integration applied to the multi-dimensional compressible Euler equations /$fSimon Markfelder 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (244 pages) 225 1 $aLecture Notes in Mathematics ;$vv.2294 311 $a3-030-83784-X 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- Contents -- Part I The Problem Studied in This Book -- 1 Introduction -- 1.1 The Euler Equations -- 1.2 Weak Solutions and Admissibility -- 1.3 Overview on Well-Posedness Results -- 1.4 Structure of This Book -- 2 Hyperbolic Conservation Laws -- 2.1 Formulation of a Conservation Law -- 2.2 Initial Boundary Value Problem -- 2.3 Hyperbolicity -- 2.4 Companion Laws and Entropies -- 2.5 Admissible Weak Solutions -- 3 The Euler Equations as a Hyperbolic Systemof Conservation Laws -- 3.1 Barotropic Euler System -- 3.1.1 Hyperbolicity -- 3.1.2 Entropies -- 3.1.3 Admissible Weak Solutions -- 3.2 Full Euler System -- 3.2.1 Hyperbolicity -- 3.2.2 Entropies -- 3.2.3 Admissible Weak Solutions -- Part II Convex Integration -- 4 Preparation for Applying Convex Integrationto Compressible Euler -- 4.1 Outline and Preliminaries -- 4.1.1 Adjusting the Problem -- 4.1.2 Tartar's Framework -- 4.1.3 Plane Waves and the Wave Cone -- 4.1.4 Sketch of the Convex Integration Technique -- 4.2 -Convex Hulls -- 4.2.1 Definitions and Basic Facts -- 4.2.2 The HN-Condition and a Way to Define U -- 4.2.3 The -Convex Hull of Slices -- 4.2.4 The -Convex Hull if the Wave Cone is Complete -- 4.3 The Relaxed Set U Revisited -- 4.3.1 Definition of U -- 4.3.2 Computation of U -- 4.4 Operators -- 4.4.1 Statement of the Operators -- 4.4.2 Lemmas for the Proof of Proposition 4.4.1 -- 4.4.3 Proof of Proposition 4.4.1 -- 5 Implementation of Convex Integration -- 5.1 The Convex-Integration-Theorem -- 5.1.1 Statement of the Theorem -- 5.1.2 Functional Setup -- 5.1.3 The Functionals I0 and the Perturbation Property -- 5.1.4 Proof of the Convex-Integration-Theorem -- 5.2 Proof of the Perturbation Property -- 5.2.1 Lemmas for the Proof -- 5.2.2 Proof of Lemma 5.2.4 -- 5.2.3 Proof of Lemma 5.2.1 Using Lemmas 5.2.2, 5.2.3and 5.2.4. 327 $a5.2.4 Proof of the Perturbation Property Using Lemma 5.2.1 -- 5.3 Convex Integration with Fixed Density -- 5.3.1 A Modified Version of the Convex-Integration-Theorem -- 5.3.2 Proof the Modified Perturbation Property -- Part III Application to Particular Initial (Boundary) Value Problems -- 6 Infinitely Many Solutions of the Initial Boundary Value Problem for Barotropic Euler -- 6.1 A Simple Result on Weak Solutions -- 6.2 Possible Improvements to Obtain Admissible Weak Solutions -- 6.3 Further Possible Improvements -- 7 Riemann Initial Data in Two Space Dimensionsfor Isentropic Euler -- 7.1 One-Dimensional Self-Similar Solution -- 7.2 Summary of the Results on Non-/Uniqueness -- 7.3 Non-Uniqueness Proof if the Self-Similar Solution Consists of One Shock and One Rarefaction -- 7.3.1 Condition for Non-Uniqueness -- 7.3.2 The Corresponding System of Algebraic Equations and Inequalities -- 7.3.3 Simplification of the Algebraic System -- 7.3.4 Solution of the Algebraic System if the Rarefaction is ``Small'' -- 7.3.5 Proof of Theorem 7.3.1 via an Auxiliary State -- 7.4 Sketches of the Non-Uniqueness Proofs for the Other Cases -- 7.4.1 Two Shocks -- 7.4.2 One Shock -- 7.4.3 A Contact Discontinuity and at Least One Shock -- 7.5 Other Results in the Context of the Riemann Problem -- 8 Riemann Initial Data in Two Space Dimensions for Full Euler -- 8.1 One-Dimensional Self-Similar Solution -- 8.2 Summary of the Results on Non-/Uniqueness -- 8.3 Non-Uniqueness Proof if the Self-Similar Solution Contains Two Shocks -- 8.3.1 Condition for Non-Uniqueness -- 8.3.2 The Corresponding System of Algebraic Equations and Inequalities -- 8.3.3 Solution of the Algebraic System -- 8.4 Sketches of the Non-Uniqueness Proofs for the Other Cases -- 8.4.1 One Shock and One Rarefaction -- 8.4.2 One Shock -- 8.5 Other Results in the Context of the Riemann Problem. 327 $aA Notation and Lemmas -- A.1 Sets -- A.2 Vectors and Matrices -- A.2.1 General Euclidean Spaces -- A.2.2 The Physical Space and the Space-Time -- A.2.3 Phase Space -- A.3 Sequences -- A.4 Functions -- A.4.1 Basic Notions -- A.4.2 Differential Operators -- Functions of Time and Space -- Functions of the State Vector -- A.4.3 Function Spaces -- A.4.4 Integrability Conditions -- A.4.5 Boundary Integrals and the Divergence Theorem -- A.4.6 Mollifiers -- A.4.7 Periodic Functions -- A.5 Convexity -- A.5.1 Convex Sets and Convex Hulls -- A.5.2 Convex Functions -- A.6 Semi-Continuity -- A.7 Weak- Convergence in L? -- A.8 Baire Category Theorem -- Bibliography -- Index. 410 0$aLecture Notes in Mathematics 606 $aDifferential equations 606 $aPhysics 606 $aGlobal analysis (Mathematics) 606 $aEquacions de Lagrange$2thub 606 $aFuncions convexes$2thub 606 $aIntegració numčrica$2thub 606 $aProblemes de contorn$2thub 608 $aLlibres electrņnics$2thub 615 0$aDifferential equations. 615 0$aPhysics. 615 0$aGlobal analysis (Mathematics) 615 7$aEquacions de Lagrange 615 7$aFuncions convexes 615 7$aIntegració numčrica 615 7$aProblemes de contorn 676 $a515.35 686 $a35Q31$2msc 686 $a76N10$2msc 686 $a35L65$2msc 686 $a35L45$2msc 686 $a35L50$2msc 700 $aMarkfelder$b Simon$0854270 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466386703316 996 $aConvex Integration Applied to the Multi-Dimensional Compressible Euler Equations$91907599 997 $aUNISA