scholarly journals Exact Steady Solutions for the Two Dimensional Broadwell Model

2019 ◽  
pp. 1-14
Author(s):  
Amah Séna D'Almeida ◽  
Kokou Anani Agosseme
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Analytic Solutions ◽  
Two Dimensional ◽  
Exact Analytic Solutions ◽  
Accommodation Coefficients ◽  
Steady Solutions

Existence and boundedness of the solutions of the boundary value problem for the four velocity two dimensional Broadwell model for bounded boundary conditions is proved and exact analytic solutions are built. An application to the determination of the accommodation coefficients on the boundaries of a flow in a box is performed.

scholarly journals Parametrization for some boundary value problems of interpolation type

2009 ◽  
Vol 43 (1) ◽  
pp. 229-242
Author(s):  
Miklós Rontó ◽  
Natalia Shchobak
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Analytic Form ◽  
Successive Approximations ◽  
Two Dimensional ◽  
Linear Boundary ◽  
Scalar Parameter ◽  
The Given

Abstract We obtain some results concerning the investigation of two-dimensional non-linear boundary value problems of interpolation type. We show that it is useful to reduce the given boundary value problem, using an appropriate substitution, to a parametrized boundary value problem containing some unknown scalar parameter in the boundary conditions. To study the transformed parametrized problem, we use a method which is based upon special types of successive approximations constructed in an analytic form.

EXISTENCE OF SOLUTIONS OF A BOUNDARY VALUE PROBLEM FOR THE FOUR VELOCITY BROADWELL MODEL

2021 ◽  
Vol 10 (11) ◽  
pp. 3409-3438
Author(s):  
A.E. Nicoué ◽  
A.S. d’Almeida
Keyword(s):  
Fluid Flow ◽  
Boundary Value Problem ◽  
Exact Solutions ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Two Dimensional ◽  
Accommodation Coefficients

Existence and boundedness is proved for the solutions of a boundary value problem for the two-dimensional Broadwell model in a rectangle. The influence of the orientation of the model in relation to the sides of the rectangle on the form of the boundary value problem is analysed. Exact solutions are found and use to determine accommodation coefficients at the boundaries of a fluid flow in a rectangular box.

scholarly journals Eigenvalues of the Laplacian for the third boundary value problem

1987 ◽  
Vol 29 (1) ◽  
pp. 79-87 ◽  
Author(s):  
E. M. E. Zayed
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Spectral Function ◽  
Boundary Value ◽  
Two Dimensional ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions ◽  
The Third ◽  
Eigenvalues Of The Laplacian ◽  
Third Boundary Value Problem

AbstractThe spectral function , where are the eigenvalues of the two-dimensional Laplacian, is studied for a variety of domains. The dependence of θ(t) on the connectivity of a domain and the impedance boundary conditions is analysed. Particular attention is given to a doubly-connected region together with the impedance boundary conditions on its boundaries.

On the solution to a two-dimensional boundary value problem of heat conduction in a degenerating domain

2020 ◽  
Vol 98 (2) ◽  
pp. 100-109
Author(s):  
Minzilya T. Kosmakova ◽  
◽  
Valery G. Romanovski ◽  
Dana M. Akhmanova ◽  
Zhanar M. Tuleutaeva ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Two Dimensional ◽  
Dimensional Boundary

Identification of the string boundary conditions using natural frequencies

2016 ◽  
Vol 11 (1) ◽  
pp. 38-52
Author(s):  
I.M. Utyashev ◽  
A.M. Akhtyamov
Keyword(s):  
Inverse Problems ◽  
Power Series ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Boundary Value ◽  
External Environment ◽  
Direct And Inverse Problems ◽  
Symmetric Potential ◽  
Modified Method

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

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.

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