scholarly journals Solvability Analysis of a Mixed Boundary Value Problem for Stationary Magnetohydrodynamic Equations of a Viscous Incompressible Fluid

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2088
Author(s):  
Gennadii Alekseev ◽  
Roman V. Brizitskii
Keyword(s):  
Boundary Value Problem ◽  
A Priori Estimates ◽  
Mixed Boundary ◽  
Boundary Value ◽  
A Priori ◽  
Sufficient Conditions ◽  
Mixed Boundary Conditions ◽  
Global Solvability ◽  
Tangential Component ◽  
Mhd Equations

We investigate the boundary value problem for steady-state magnetohydrodynamic (MHD) equations with inhomogeneous mixed boundary conditions for a velocity vector, given the tangential component of a magnetic field. The problem represents the flow of electrically conducting viscous fluid in a 3D-bounded domain, which has the boundary comprising several parts with different physical properties. The global solvability of the boundary value problem is proved, a priori estimates of the solutions are obtained, and the sufficient conditions on data, which guarantee a solution’s local uniqueness, are determined.

scholarly journals The nonlocal boundary value problem with perturbations of mixed boundary conditions for an elliptic equation with constant coefficients. II

2020 ◽  
Vol 12 (1) ◽  
pp. 173-188
Author(s):  
Ya.O. Baranetskij ◽  
P.I. Kalenyuk ◽  
M.I. Kopach ◽  
A.V. Solomko
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Mixed Boundary Conditions ◽  
Multipoint Problem ◽  
Uniqueness Of The Solution

In this paper we continue to investigate the properties of the problem with nonlocal conditions, which are multipoint perturbations of mixed boundary conditions, started in the first part. In particular, we construct a generalized transform operator, which maps the solutions of the self-adjoint boundary-value problem with mixed boundary conditions to the solutions of the investigated multipoint problem. The system of root functions $V(L)$ of operator $L$ for multipoint problem is constructed. The conditions under which the system $V(L)$ is complete and minimal, and the conditions under which it is the Riesz basis are determined. In the case of an elliptic equation the conditions of existence and uniqueness of the solution for the problem are established.

scholarly journals On a semi-nonlocal boundary value problem for the three-dimensional Tricomi equation of an unbounded prismatic domain

2021 ◽  
pp. 8-16
Author(s):  
С.З. Джамалов ◽  
Р.Р. Ашуров ◽  
Х.Ш. Туракулов
Keyword(s):  
Boundary Value Problem ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Three Dimensional ◽  
Generalized Solution ◽  
Nonlocal Boundary Value Problem ◽  
Tricomi Equation ◽  
The Fourier Transform

В данной статье изучаются методами «ε-регуляризации» и априорных оценок с применением преобразования Фурье однозначная разрешимость и гладкость обобщенного решения одной полунелокальной краевой задачи для трехмерного уравнения Трикоми в неограниченной призматической области. In this article, the methods of «ε-regularization» and a priori estimates using the Fourier transform are studied the unique solvability and smoothness of the generalized solution of one semi-nonlocal boundary value problem for the three-dimensional Tricomi equation in an unbounded prismatic domain.

scholarly journals Existence and uniqueness of solutions for a fractional boundary value problem on a graph

2014 ◽  
Vol 17 (2) ◽  
Author(s):  
John Graef ◽  
Lingju Kong ◽  
Min Wang
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Conditions ◽  
Point Theory ◽  
Star Graph ◽  
Fractional Boundary Value Problem ◽  
Uniqueness Of Solutions

AbstractIn this paper, the authors consider a nonlinear fractional boundary value problem defined on a star graph. By using a transformation, an equivalent system of fractional boundary value problems with mixed boundary conditions is obtained. Then the existence and uniqueness of solutions are investigated by fixed point theory.

scholarly journals A robust linearisation scheme for a nonlinear elliptic boundary value problem: Error estimates

2005 ◽  
Vol 46 (4) ◽  
pp. 449-470 ◽  
Author(s):  
Marian Slodička
Keyword(s):  
Boundary Value Problem ◽  
Error Estimates ◽  
Mixed Boundary ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Mixed Boundary Conditions ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Nonlinear Elliptic ◽  
Nonlinear Elliptic Boundary

AbstractWe consider a nonlinear second-order elliptic boundary value problem in a bounded domain Ω ⊂ RN with mixed boundary conditions. The solution is found via linearisation. We design a robust and efficient approximation scheme. Error estimates for the linearisation algorithm are derived in L2(Ω), H1(Ω) and L∞(Ω) spaces under the minimal regularity assumptions of the exact solution.

scholarly journals A Boundary Value Problem with Multivariables Integral Type Condition for Parabolic Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-13
Author(s):  
A. L. Marhoune ◽  
F. Lakhal
Keyword(s):  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Continuous Dependence ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Analysis Method ◽  
Type Condition ◽  
Integral Type ◽  
Priori Estimates

We study a boundary value problem with multivariables integral type condition for a class of parabolic equations. We prove the existence, uniqueness, and continuous dependence of the solution upon the data in the functional wieghted Sobolev spaces. Results are obtained by using a functional analysis method based on two-sided a priori estimates and on the density of the range of the linear operator generated by the considered problem.

A Discreate Calculus with Applications of High-Order Discretizations to Boundary-Value Problems

2004 ◽  
Vol 4 (2) ◽  
pp. 228-261 ◽  
Author(s):  
Stanly Steinberg
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Energy Inequality ◽  
Numerical Test ◽  
Mixed Boundary Conditions ◽  
Discrete Analog ◽  
High Order ◽  
Sturm Liouville

AbstractWe develop a discrete analog of the differential calculus and use this to develop arbitrarily high-order approximations to Sturm–Liouville boundary-value problems with general mixed boundary conditions. An important feature of the method is that we obtain a discrete exact analog of the energy inequality for the continuum boundary-value problem. As a consequence, the discrete and continuum problems have exactly the same solvability conditions. We call such discretizations mimetic. Numerical test confirm the accuracy of the discretization. We prove the solvability and convergence for the discrete boundary-value problem modulo the invertibility of a matrix that appears in the discretization being positive definite. Numerical experiments indicate that the spectrum of this matrix is real, greater than one, and bounded above by a number smaller than three.

Sign in / Sign up

Export Citation Format

Share Document