Estimates for Pseudo-differential and Hyperbolic Differential Equations via Fourier Integrals with Complex Phases

2001 ◽  
pp. 831-839
Author(s):  
Michael Ruzhansky
Keyword(s):  
Differential Equations ◽  
Hyperbolic Differential Equations ◽  
Fourier Integrals

Mixed Problems for Linear Systems of first Order Equations

1958 ◽  
Vol 10 ◽  
pp. 127-160 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Auxiliary Data ◽  
First Order ◽  
Independent Variables ◽  
Mixed Problems ◽  
Linear Partial Differential Equations ◽  
Data Problem ◽  
Hyperbolic Differential Equations

A mixed problem in the theory of partial differential equations is an auxiliary data problem wherein conditions are assigned on two distinct surfaces having an intersection of lower dimension. Such problems have usually been formulated in connection with hyperbolic differential equations, with initial and boundary conditions prescribed. In this paper a study is made of the conditions appropriate to a system of R linear partial differential equations of first order, in R dependent and N independent variables.

Piecewise Analytic Solutions of Mixed Boundary Value Problems

1966 ◽  
Vol 18 ◽  
pp. 1121-1147 ◽  
Author(s):  
M. Eisen
Keyword(s):  
Differential Equations ◽  
Mixed Problem ◽  
Mixed Boundary ◽  
Separation Of Variables ◽  
Analytic Solutions ◽  
General Criterion ◽  
Method Of Images ◽  
Correct Boundary Conditions ◽  
Hyperbolic Differential Equations ◽  
Boundary Surfaces

In a mixed problem one is required to find a solution of a system of partial differential equations when the values of certain combinations of the derivatives are given on two or more distinct intersecting surfaces. If the differential equations arise from some physical process, the correct boundary conditions are usually apparent. Many particular problems of this type have been solved by special methods such as separation of variables and the method of images. However, no general criterion has been given for what constitutes a correctly set mixed problem. In fact such problems have usually been formulated in connection with hyperbolic differential equations with data prescribed on two surfaces (called the initial and boundary surfaces).

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