双曲型偏微分方程和几何光学(影印版)

Preface §P.1.How this book came to be, and its peculiarities §P.2.A bird's eye view of hyperbolic equations Chapter 1.Simple Examples of Propagation §1.1.The method of characteristics §1.2.Examples of propagation of singularities using progressing waves §1.3.Group velocity and the method of nonstationary phase §1.4.Fourier synthesis and rectilinear propagation §1.5.A cautionary example in geometric optics §1.6.The law of reflection 1.6.1.The method of images 1.6.2.The plane wave derivation 1.6.3.Reflected high frequency wave packets §1.7.Snell's law of refraction Chapter 2.The Linear Cauchy Problem §2.1.Energy estimates for symmetric hyperbolic systems §2.2.Existence theorems for symmetric hyperbolic systems 62.3.Finite speed of propagation 2.3.1.The method of characteristics 2.3.2.Speed estimates uniform in space 2.3.3.Time-like and propagation cones §2.4.Plane waves, group velocity, and phase velocities §2.5.Precise speed estimate §2.6.Local Cauchy problems Appendix 2.I.Constant coefficient hyperbolic systems Appendix 2.II.Functional analytic proof of existence Chapter 3.Dispersive Behavior §3.1.Orientation §3.2.Spectral decomposition of solutions §3.3.Large time asymptotics §3.4.Maximally dispersive systems 3.4.1.The L1 → Lo decay estimate 3.4.2.Fixed time dispersive Sobolev estimates 3.4.3.Strichartz estimates Appendix 3.I.Perturbation theory for semisimple eigenvalues Appendix 3.IⅡ.The stationary phase inequality Chapter 4.Linear Elliptic Geometric Optics §4.1.Euler's method and elliptic geometric optics with constant coefficients §4.2.Iterative improvement for variable coefficients and nonlinear phases §4.3.Formal asymptotics approach §4.4.Perturbation approach §4.5.Elliptic regularity §4.6.The Microlocal Elliptic Regularity Theorem Chapter 5.Linear Hyperbolic Geometric Optics §5.1.Introduction §5.2.Second order scalar constant coefficient principal part 5.2.1.Hyperbolic problems 5.2.2.The quasiclassical limit of quantum mechanics §5.3.Symmetric hyperbolic systems §5.4.Rays and transport