Author | Majda, A. author |
---|---|
Title | Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables [electronic resource] / by A. Majda |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1984 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1116-7 |
Descript | 172 p. online resource |
1. Introduction -- 1.1. Some Physical Examples of Systems of Conservation Laws -- 1.2. The Importance of Dissipative Mechanisms -- 1.3. The Common Structure of the Physical Systems of Conservation Laws and Friedrichsโ Theory of Symmetric Systems -- 1.4. Linear and Nonlinear Wave Propagation and the Theory of Nonlinear Simple Waves -- 1.5. Weakly Nonlinear Asymptotics โ Nonlinear Geometric Optics -- 1.6. A Rigorous Justification of Weakly Nonlinear Asymptotics in a Special Case -- 1.7. Some Additional Applications of Weakly Nonlinear Asymptotics in the Modeling of Complex Systems -- Bibliography for Chapter 1 -- 2. Smooth Solutions and the Equations of Incompressible Fluid Flow -- 2.1. The Local Existence of Smooth Solutions for Systems of Conservation Laws -- 2.2. A Continuation Principle for Smooth Solutions 46 2.3. Uniformly Local Sobolev Spaces -- 2.4. Compressible and Incompressible Fluid Flow -- 2.5. Equations for Low Mach Number Combustion -- Bibliography for Chapter 2 -- 3. The Formation of Shock Waves in Smooth Solutions -- 3.1. Shock Formation for Scalar Laws in Several Space Variables -- 3.2. Shock Formation in Plane Wave Solutions of General m ร m Systems -- 3.3. Detailed Results on Shock Formation for 2 ร 2 Systems -- 3.4. Breakdown for a Quasi-Linear Wave Equation in 3-D -- 3.5. Some Open Problems Involving Shock Formation in Smooth Solutions -- Bibliography for Chapter 3 -- 4. The Existence and Stability of Shock Fronts in Several Space Variables -- 4.1. Nonlinear Discontinuous Progressing Waves in Several Variables โ Shock Front Initial Data -- 4.2. Some Theorems Guaranteeing the Existence of Shock Fronts -- 4.3. Linearization of Shock Fronts -- 4.4. An Introduction to Hyperbolic Mixed Problems -- 4.5. Quantitative Estimates for Linearized Shock Fronts -- 4.6. Some Open Problems in Multi-D Shock Wave Theory -- Bibliography for Chapter 4