The monastery tou Libos: Architecture, sculpture, and liturgical planning in middle and late Byzanti...

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" The monastery tou Libos: Architecture, sculpture, and liturgical planning in middle and late Byzantine Constantinople "
Vasileios Marinis R. Ousterhout

Document Type	:	BL
Record Number	:	573421
Doc. No	:	b402640
Main Entry	:	Zheng, Yuxi.
Title & Author	:	Systems of Conservation Laws : Two-Dimensional Riemann Problems /\ by Yuxi Zheng.
Publication Statement	:	Boston, MA :: Birkhäuser Boston :: Imprint: Birkhäuser,, 2001.
Series Statement	:	Progress in Nonlinear Differential Equations and Their Applications ;; 38
ISBN	:	9781461201410
	:	: 9781461266310
Contents	:	1 Problems -- 1.0 Outline -- 1.1 Some models -- 1.2 Basic problems -- 1.3 Some solutions -- 1.4 von Neumann paradoxes -- 1.5 End notes -- I Basics in One Dimension -- 2 One-dimensional Scalar Equations -- 3 Riemann Problems -- 4 Cauchy Problems -- II Two Dimensional Theory -- 5 A 2-D Scalar Riemann Problem -- 6 The 2-D Riemann problem and Pseudo-Characteristics -- 7 Axisymmetric and Self-similar Solutions -- 8 Plausible Structures for 2-D Euler Systems -- 9 The Pressure-Gradient Equations of the Euler Systems -- 10 The Convective Systems of the Euler Systems -- 11 The Two-dimensional Burgers Equations -- III Numerical schemes -- 12 Numerical Approaches -- List of Symbols.
Abstract	:	This work is based on the lecture notes of the course M742: Topics in Partial Dif ferential Equations, which I taught in the Spring semester of 1997 at Indiana Univer sity. My main intention in this course was to give a concise introduction to solving two-dimensional compressibleEuler equations with Riemann data, which are special Cauchy data. This book covers new theoretical developments in the field over the past decade or so. Necessary knowledge of one-dimensional Riemann problems is reviewed and some popularnumerical schemes are presented. Multi-dimensional conservation laws are more physical and the time has come to study them. The theory onbasicone-dimensional conservation laws isfairly complete providing solid foundation for multi-dimensional problems. The rich theory on ellip tic and parabolic partial differential equations has great potential in applications to multi-dimensional conservation laws. And faster computers make itpossible to reveal numerically more details for theoretical pursuitin multi-dimensional problems. Overview and highlights Chapter 1is an overview ofthe issues that concern us inthisbook. It lists theEulersystemandrelatedmodelssuch as theunsteady transonic small disturbance, pressure-gradient, and pressureless systems. Itdescribes Mach re flection and the von Neumann paradox. In Chapters 2-4, which form Part I of the book, we briefly present the theory of one-dimensional conservation laws, which in cludes solutions to the Riemann problems for the Euler system and general strictly hyperbolic and genuinely nonlinearsystems, Glimm's scheme, and large-time asymp toties.
Subject	:	Mathematics.
Subject	:	Global analysis (Mathematics).
Subject	:	Computer science-- Mathematics.
Added Entry	:	SpringerLink (Online service)