Systems of Conservation Laws

[see attached] This work should serve as an excellent text for graduate students and researchers working in the important area of partial differential equations with a focus on problems involving conservation laws. Written in a clear, accessible style, the book emphasizes more recent results that will prepare readers to meet modern challenges in the subject, that is, to carry out theoretical, numerical, and asymptotical analysis. Key features of this work include: * broad range of topics, from the classical treatment to recent results, dealing with solutions to the 2-D compressible Euler

Klappentext

PThis work should serve as an introductory text for graduate students and researchers working in the important area of partial differential equations with a focus on problems involving conservation laws. The only requisite for the reader is a knowledge of the elementary theory of partial differential equations. /PPKey features of this work include: /PP broad range of topics, from the classical treatment to recent results, dealing with solutions to 2D compressible Euler equations /PP good review of basic concepts (1-D Riemann problems) /PP concrete solutions presented, with many examples, over 100 illustrations, open problems, and numerical schemes /PP numerous exercises, comprehensive bibliography and index /PP* appeal to a wide audience of applied mathematicians, graduate students, physicists, and engineers Written in a clear, accessible style, the book emphasizes more recent results that will prepare readers to meet modern challenges in the subject, that is, to carry out theoretical, numerical, and asymptotical analysis./P

Inhalt
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.