An Application of the Analytic Microlocal Analysis to a Class of Differential Operators of Mixed Type

1985 ◽  
Vol 121 (1) ◽  
pp. 41-51 ◽  
Author(s):  
T. V. Gramchev
Keyword(s):  
Mixed Type ◽  
Differential Operators ◽  
Microlocal Analysis ◽  
Analytic Microlocal Analysis

scholarly journals Pseudo-Differential Operators, Microlocal Analysis and Image Restoration

2004 ◽  
pp. 187-202
Author(s):  
Ryuichi Ashino ◽  
J. Steven Desjardins ◽  
Chris Heil ◽  
Michihiro Nagase ◽  
Rémi Vaillancourt
Keyword(s):  
Image Restoration ◽  
Differential Operators ◽  
Microlocal Analysis ◽  
Pseudo Differential Operators

scholarly journals Boundary Value Problems with Integral Gluing Conditions for Fractional-Order Mixed-Type Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
A. S. Berdyshev ◽  
E. T. Karimov ◽  
N. Akhtaeva
Keyword(s):  
Mixed Type ◽  
Differential Operators ◽  
Type Equation ◽  
Telegraph Equation ◽  
Fractional Diffusion ◽  
Tricomi Problem ◽  
Green Functions ◽  
Mixed Type Equation ◽  
Energy Integrals ◽  
Gellerstedt Problem

Analogs of the Tricomi and the Gellerstedt problems with integral gluing conditions for mixed parabolic-hyperbolic equation with parameter have been considered. The considered mixed-type equation consists of fractional diffusion and telegraph equation. The Tricomi problem is equivalently reduced to the second-kind Volterra integral equation, which is uniquely solvable. The uniqueness of the Gellerstedt problem is proven by energy integrals' method and the existence by reducing it to the ordinary differential equations. The method of Green functions and properties of integral-differential operators have been used.

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