scholarly journals Some properties of a Cauchy-type integral for the Moisil-Theodoresco system of partial differential equations

2006 ◽  
Vol 58 (1) ◽  
pp. 118-126 ◽  
Author(s):  
B. Schneider
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Cauchy Type ◽  
Cauchy Type Integral ◽  
Partial Differential ◽  
Type Integral

scholarly journals Of one over determined system differential equations at private derivative second order with one singular lines in general case

2021 ◽  
pp. 10-15
Author(s):  
Boitura Shoimkulov ◽  
◽  
Р. М. С. Lukmon ◽  
Keyword(s):  
Partial Differential Equations ◽  
Initial Data ◽  
Differential Equations ◽  
Compatibility Condition ◽  
Second Order ◽  
Integral Representations ◽  
Singular Line ◽  
Cauchy Type ◽  
Partial Differential

In this paper, an over determined system of second-order partial differential equations with a single singular line in the General case is investigated. A compatibility condition is found for over determined systems of second-order partial differential equations with a single singular line in the General case. If the compatibility condition is met, integral representations of the variety of solutions are found explicitly in terms of three arbitrary constants, when the singular line is in the boundaries of the domain for which initial data problems (Cauchy-type Problems) can be set.

Some second-order systems of partial differential equations of composite type

1987 ◽  
Vol 106 (1-2) ◽  
pp. 73-88 ◽  
Author(s):  
Lin Wei
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hyperbolic Systems ◽  
Second Order ◽  
Cauchy Type ◽  
Linear Transformations ◽  
Partial Differential ◽  
Composite Systems ◽  
Composite Type ◽  
Second Order Systems

SynopsisThe Cauchy problem and the Dirichlet-Cauchy type problem of some second-order systems of partial differential equations of composite type of two unknown functions are investigated. Such systems possess some of the characteristics not only of elliptic but also of hyperbolic systems in the same domain. Representations of the solutions are found for the upper half plane. To this end, the composite systems are reduced to the canonical form by means of successive applications of three kinds of linear transformations. Function theoretic methods are used to obtain representation formulae. Furthermore, some composite systems of 2m-unknown function are also considered.

scholarly journals Integral representation of solution manifolds for over determined systems with one singular line

2021 ◽  
pp. 5-9
Author(s):  
Boitura Shoimkulov ◽  
Keyword(s):  
Partial Differential Equations ◽  
Initial Data ◽  
Differential Equations ◽  
Integral Representation ◽  
Compatibility Condition ◽  
Second Order ◽  
Singular Line ◽  
Cauchy Type ◽  
Partial Differential ◽  
Partial Differential System

In this paper, an over determined system of second-order partial differential equations with one singular line is investigated. A compatibility condition is found for over determined systems of second-order partial differential equations with one singular line. Under the condition of compatibility, introducing a new function, we come to a over determined system of partial differential equations of the second order with one singular line of a simpler form. The integral representation of the manifold of solutions of the redefined second-order partial differential system with one singular line is found explicitly through three arbitrary constants, for which initial data problems (Cauchy type problems) can be posed.

scholarly journals Of one over determined system differential equation at private derivative second order with one singular point and one singular line

2021 ◽  
pp. 14-18
Author(s):  
B. M. Shoimkulov ◽  
Keyword(s):  
Partial Differential Equations ◽  
Singular Point ◽  
Differential Equations ◽  
Compatibility Condition ◽  
Second Order ◽  
Integral Representations ◽  
Singular Line ◽  
Cauchy Type ◽  
National Academy Of Sciences ◽  
Partial Differential

In this paper, a over determined system of second-order partial differential equations with one singular point and one singular line is investigated. A compatibility condition is found for over determined systems of second-order partial differential equations with one singular point and one singular line. If the compatibility condition is met, integral representations of the variety of solutions are found explicitly in terms of three arbitrary constants, when the singular line is in the boundaries of the domain for which initial data problems (Cauchy-type Problems) can be set. In this paper considers a redefined system of second-order partial differential equations, when the coefficients and right parts have one singular point and one singular line. Obtaining a variety of solutions and studying boundary value problems for linear differential equations of the hyperbolic type of the second order, some linear redefined systems of the first and second order with one and two supersingular lines and supersingular points is devoted to the monograph of academician of the National Academy of Sciences of the Republic of Tatarstan Rajabov N. - 1992 "Introduction to the theory of partial differential equations with supersingular coefficients" [6, p.126]. Using the obtained results of The monograph of Rajabov N., a variety of solutions of redefined systems of partial differential equations of the second order with one singular point and one singular line in an explicit form, through three arbitrary constants, was found.

scholarly journals On Canonical Almost Geodesic Mappings of Type π2(e)

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 54 ◽  
Author(s):  
Volodymyr Berezovski ◽  
Josef Mikeš ◽  
Lenka Rýparová ◽  
Almazbek Sabykanov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symmetric Spaces ◽  
Riemann Tensor ◽  
Mixed System ◽  
Cauchy Type ◽  
Partial Differential ◽  
Affine Connections

In the paper, we consider canonical almost geodesic mappings of type π 2 ( e ) . We have found the conditions that must be satisfied for the mappings to preserve the Riemann tensor. Furthermore, we consider canonical almost geodesic mappings of type π 2 ( e ) of spaces with affine connections onto symmetric spaces. The main equations for the mappings are obtained as a closed mixed system of Cauchy-type Partial Differential Equations. We have found the maximum number of essential parameters which the solution of the system depends on.

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