CHARACTERISTIC FUNCTION OF THE SYSTEM D–EQUATIO

2021 ◽  
Vol 75 (3) ◽  
pp. 29-34
Author(s):  
Р. С. Ysmagul ◽  
◽  
B.O. Zhumartova ◽  
Keyword(s):  
Characteristic Function ◽  
Periodic Solutions ◽  
Vector Function ◽  
Lipschitz Condition ◽  
Existence And Uniqueness ◽  
Mathematical Physics ◽  
Evolutionary Equation ◽  
Bounded Solutions ◽  
Evolutionary Equations ◽  
Equations Of Mathematical Physics

This paper is devoted to the problems of studying the multiperiodic solution of some evolutionary equations. The article also discusses the existence and uniqueness of a multiperiodic solution with respect to vector functions for an evolutionary reduced equation. Studies have been conducted on the characteristic function of a certain system of the evolutionary equation. Some properties of the vector function are proved. They can be used in the further study of oscillatory bounded solutions of evolutionary equations. Based on the argumentation of the theorem on the existence and uniqueness of an almost multiperiodic solution of the specified system, considered using the method of shortening the characteristic function. All estimates of the characteristic function are based on the enhanced Lipschitz condition, first introduced by academician K. P. Persidskiy. The results will also be useful in the study of periodic solutions of evolutionary equations of mathematical physics

H-measures applied to symmetric systems

1996 ◽  
Vol 126 (6) ◽  
pp. 1133-1155 ◽  
Author(s):  
Nenad Antonić
Keyword(s):  
Wave Equation ◽  
Vector Function ◽  
Mathematical Physics ◽  
Symmetric System ◽  
Matrix Functions ◽  
Equations Of Mathematical Physics ◽  
Image Position ◽  
Unknown Vector ◽  
Second Order Equations ◽  
Symmetric Systems

H-measures were recently introduced by Luc Tartar as a tool which might provide better understanding of propagating oscillations. Independently, Patrick Gerard introduced the same objects under the name of microlocal defect measures. Partial differential equations of mathematical physics can often be written in the form of a symmetric system:where Ak and B are matrix functions, while u is an unknown vector function, and f a known vector function. In this work we prove a general propagation theorem for H-measures associated to symmetric systems. This result, combined with the localisation property, is then used to obtain more precise results on the behaviour of H-measures associated to the wave equation, Maxwell's and Dirac's systems, and second-order equations in two variables.

scholarly journals THE RESIDUE THEOREM AND AN ANALOG OF P. APPELL’S FORMULA FOR FINITE RIEMANN SURFACES

2016 ◽  
pp. 40-45
Author(s):  
Viktor Chueshev ◽  
Viktor Chueshev ◽  
Aleksandr Chueshev ◽  
Aleksandr Chueshev
Keyword(s):  
Riemann Surfaces ◽  
Meromorphic Functions ◽  
Function Theory ◽  
Mathematical Physics ◽  
General Function ◽  
Multiplicative Functions ◽  
Residue Theorem ◽  
Equations Of Mathematical Physics ◽  
Compact Riemann Surfaces ◽  
Integral Order

A theory of multiplicative functions and Prym differentials for the case of special characters on compact Riemann surfaces has found applications in geometrical function theory of complex variable, analytical number theory and in equations of mathematical physics. Theory of functions on compact Riemann surfaces differs from the theory of functions on finite Riemann surfaces even for the class of single meromorphic functions and Abelian differentials. In this article we continue the construction of the general function theory on finite Riemann surfaces for multiplicative meromorphic functions and differentials. We have proved analogues of the theorem on the full sum of residues for Prym differentials of every integral order and P. Appell's formula on expansion of the multiplicative function with poles of arbitrary multiplicity in the sum of elementary Prym integrals.

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