Palamodov V. Topics in Mathematical Physics

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2002. - 80 с.

Представленная на английском языке работа - курс лекций Паламодова, подробно объясняющая решение уравнений математической физики из 8 частей.

Contents
Chapter 1: Differential equations of Mathematical Physics
Differential equations of elliptic type
Diffusion equations
Wave equations
Systems
Nonlinear equations
Hamilton-Jacobi theory
Relativistic field theory
Classification
Initial and boundary value problems
Inverse problems

Chapter 2: Elementary methods
Change of variables
Bilinear integrals
Conservation laws
Method of plane waves
Fourier transform
Theory of distributions

Chapter 3: Fundamental solutions
Basic definition and properties
Fundamental solutions for elliptic operators
More examples
Hyperbolic polynomials and source functions
Wave propagators
Inhomogeneous hyperbolic operators
Riesz groups

Chapter 4: The Cauchy problem
Definitions
Cauchy problem for distributions
Hyperbolic Cauchy problem
Solution of the Cauchy problem for wave equations
Domain of dependence

Chapter 5: Helmholtz equation and scattering
Time-harmonic waves
Source functions
Radiation conditions
Scattering on obstacle
Interference and difraction

Chapter 6: Geometry of waves
Wave fronts
Hamilton-Jacobi theory
Geometry of rays
An integrable case
Legendre transformation and geometric duality
Fermat principle
The major Huygens principle
Geometrical optics
Caustics
Geometrical conservation law

Chapter 7: The method of Fourier integrals
Elements of symplectic geometry
Generating functions
Fourier integrals
Lagrange distributions
Hyperbolic Cauchy problem revisited

Chapter 8: Electromagnetic waves
Vector analysis
Maxwell equations
Harmonic analysis of solutions
Cauchy problem
Local conservation laws

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