Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients

✍ Scribed by Yu. V. Egorov, M. A. Shubin (auth.), Yu. V. Egorov U.F.R. M.I.G., M. A. Shubin (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1994
• Tongue: English
• Leaves: 269
• Series: Encyclopaedia of Mathematical Sciences 31
• Edition: 1
• Category: Library

✦ Synopsis

This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.

✦ Table of Contents

Front Matter....Pages i-vii
Linear Partial Differential Equations. Elements of the Modern Theory....Pages 1-120
Linear Partial Differential Equations with Constant Coefficients....Pages 121-255
Wave Front of a Distribution and Simplest Theorems on Propagation of Singularities....Pages 44-48
Fourier Integral Operators....Pages 48-60
Pseudo differential Operators of Principal Type....Pages 60-65
Mixed Problems for Hyperbolic Equations....Pages 65-78
Method of Stationary Phase and Short-wave Asymptotics....Pages 78-96
Asymptotics of Eigenvalues of Self-adjoint Differential and Pseudodifferential Operators....Pages 96-120
Generalized Functions and Fundamental Solutions of Differential Equations....Pages 128-149
Fourier Transformation of Generalized Functions....Pages 149-164
Existence and Uniqueness of Solutions of Differential Equations....Pages 164-185
The Function P + λ for Polynomials of Second-degree and its Application in the Construction of Fundamental Solutions....Pages 185-212
Boundary-value Problems in Half-space....Pages 212-240
Sharp and Diffusion Fronts of Hyperbolic Equations1....Pages 240-250
Back Matter....Pages 257-266

✦ Subjects

Analysis; Mathematical Methods in Physics; Numerical and Computational Physics