Existence and uniqueness of the solution of the initial and boundary value problem for the Boltzmann kinetic equation in the spatially inhomogeneous case

1974 ◽  
Vol 14 (2) ◽  
pp. 247-256
Author(s):  
V. I. Skakauskas
Keyword(s):  
Kinetic Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Boltzmann Kinetic Equation ◽  
Spatially Inhomogeneous ◽  
Uniqueness Of The Solution

scholarly journals Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Computational Tools ◽  
Numerical Examples ◽  
Odd Order ◽  
Uniqueness Of The Solution ◽  
Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

ON THE FIRST BOUNDARY VALUE PROBLEM FOR THE CLASS OF ELLIPTIC SYSTEMS DEGENERATING AT AN INNER POINT

2001 ◽  
Vol 6 (1) ◽  
pp. 147-155 ◽  
Author(s):  
S. Rutkauskas
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Elliptic Systems ◽  
Second Order ◽  
Type Problem ◽  
Dirichlet Type ◽  
Holder Class ◽  
Uniqueness Of The Solution ◽  
Dirichlet Type Problem

The Dirichlet type problem for the weakly related elliptic systems of the second order degenerating at an inner point is discussed. Existence and uniqueness of the solution in the Holder class of the vector‐functions is proved.

scholarly journals The second boundary value problem in a half-strip for a B-parabolic equation with the Gerasimov–Caputo time derivative

2020 ◽  
pp. 37-50
Author(s):  
Ф.Г. Хуштова
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Integral Transform ◽  
Boundary Value ◽  
Time Derivative ◽  
Half Strip ◽  
Uniqueness Of The Solution ◽  
Solution Representation ◽  
Class Of Functions

В работе исследуется вторая краевая задача в полуполосе для параболического уравнения с оператором Бесселя, действующим по пространственной переменной, и частной производной Герасимова–Капуто по времени. Доказаны теоремы существования и единственности решения рассматриваемой задачи. Представление решения найдено в терминах интегрального преобразования с функцией Райта в ядре. Единственность решения доказана в классе функций быстрого роста. При частных значениях параметров, содержащихся в рассматриваемом уравнении, последнее совпадает с классическим уравнением диффузии. In the present paper, we investigate the second boundary value problem in a half-strip for a parabolic equation with the Bessel operator acting with respect to the spatial variable and the Gerasimov–Caputo partial time derivative. Theorems of existence and uniqueness of the solution of the problem under consideration are proved.The solution representation is found in terms of an integral transform with the Wright function in the kernel. The uniqueness of the solution is proved in the class of functions of rapid growth. The considered equation for particular values of the parameters coincides with the classical diffusion equation.

scholarly journals On the weighted boundary value problem for systems of degenerate ordinary differential equations

2010 ◽  
Vol 51 ◽  
Author(s):  
Stasys Rutkauskas ◽  
Igor Saburov
Keyword(s):  
Singular Point ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Linear Equations ◽  
System Of Equations ◽  
The Matrix ◽  
Uniqueness Of The Solution ◽  
Weighted Boundary ◽  
Well Posed

A system of ordinary second order linear equations with a singular point is considered. The aim of this work is such that the system of eigenvectors of the matrix that couples the system of equations is not complete. That implies a matter of the statement of a weighted boundary value problem for this system. The well-posed boundary value problem is proposed in the article. The existence and uniqueness of the solution is proved.

scholarly journals ON THE SOLVABILITY OF SOME BOUNDARY VALUE PROBLEMS WITH INVOLUTION

2020 ◽  
Vol 26 (3) ◽  
pp. 7-16
Author(s):  
K. Zh. Nazarova ◽  
B. Kh. Turmetov ◽  
K. I. Usmanov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Laplace Operator ◽  
Poisson Equation ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Boundary Operator ◽  
Uniqueness Of The Solution ◽  
The Laplace Operator

This article is devoted to the study of the solvability of some boundary value problems with involution.In the space Rn, the map Sx=x is introduced. Using this mapping, a nonlocal analogue of the Laplace operator is introduced, as well as a boundary operator with an inclined derivative. Boundary-value problems are studied that generalize the well-known problem with an inclined derivative. Theorems on the existence and uniqueness of the solution of the problems under study are proved. In the Helder class, the smoothness of the solution is also studied. Using well-known statements about solutions of a boundary value problem with an inclined derivative for the classical Poisson equation, exact orders of smoothness of a solution to the problem under study are found.

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