Partial Differential Equations II: Elements of the Modern Theory, Equations With Constant Coefficients (Encyclopaedia of Mathematical Sciences)

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. The book 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. I. Linear Partial Differential Equations. Elements Of The Modern Theory / Yu. V. Egorov And M.a. Shubin -- Ii. Linear Partial Differential Equations With Constant Coefficients / A.i. Komech. Yu.v. Egorov, M.a. Shubin (eds.) Includes Bibliographical References And Indexes. This book presents a survey of the theory of general linear partial differential equations and, in particular, of equations with constant coefficients. It is written for researchers and graduate students in mathematics and theoretical physics. We shall use the following standard symbols.