LINEAR CONJUGATION PROBLEM WITH MULTIPOINT NONLOCAL CONDITION FOR A PARABOLIC-HYPERBOLIC EQUATION IN CYLINDRICAL DOMAIN

2021 ◽  
pp. 16-28
Author(s):  
I. Ya. Savka ◽  
R. V. Shevchyk ◽  
I. R. Tymkiv
Keyword(s):  
Hyperbolic Equation ◽  
Nonlocal Condition ◽  
Cartesian Product ◽  
Time Variable ◽  
Cylindrical Domain ◽  
Conjugation Problem ◽  
Linear Conjugation ◽  
Time Segment ◽  
Linear Conjugation Problem ◽  
Almost All

The linear conjugation problem with multipoint nonlocal condition in the time variable for a mixed parabolic-hyperbolic equation of the second order in a cylindrical domain, which is Cartesian product of the time segment and the spatial multidimensional torus, is investigated. The conditions of the existence and uniqueness of а solution to the problem in the scale of Sobolev spaces are obtained. It has been proved that these conditions fulfill for almost all (with respect to the Lebesgue measure) values of the left node of the multipoint condition.

ON R-LINEAR CONJUGATION PROBLEM ON THE UNIT CIRCLE

2020 ◽  
Vol 11 (3) ◽  
pp. 79-88
Author(s):  
Leonid Primachuk ◽  
◽  
Sergei Rogosin ◽  
Maryna Dubatovskaya ◽  
◽  
...  
Keyword(s):  
Unit Circle ◽  
Conjugation Problem ◽  
Linear Conjugation ◽  
Linear Conjugation Problem

A generalised Milne-Thomson theorem for the case of an elliptical inclusion

2012 ◽  
Vol 23 (4) ◽  
pp. 469-484 ◽  
Author(s):  
Yu. V. OBNOSOV ◽  
A. V. FADEEV
Keyword(s):  
Analytical Solutions ◽  
Meromorphic Functions ◽  
Conjugation Problem ◽  
Linear Conjugation ◽  
Exact Analytical Solutions ◽  
Linear Conjugation Problem ◽  
Elliptical Inclusion ◽  
Principal Parts ◽  
The Given ◽  
Infinite Planar

An ℝ-linear conjugation problem modelling the process of power fields forming in a heterogeneous infinite planar structure with an elliptical inclusion is considered. Exact analytical solutions are derived in the class of piece-wise meromorphic functions with their principal parts fixed. Cases with internal singularities and with singularities of the given principal parts at the interface are investigated.

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