scholarly journals A priori estimates of the solutions of nonlocal boundary value problems for a pseudo-parabolic equation

2013 ◽  
Author(s):  
М.Х. Бештоков
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problems ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problems ◽  
Priori Estimates

В работе рассматриваются нелокальные краевые задачи для псевдопараболического уравнения третьего порядка с переменными коэффициентами в одномерном и многомерном случаях. Для нелокальных задач получены априорные оценки в дифференциальной и разностной трактовках. Из полученных оценок следуют единственность, устойчивость, а также сходимость решения разностной задачи к решению дифференциальной задачи.

scholarly journals Boundary value problems with nonlocal conditions for hyperbolic systems of equations with two independent variables

2020 ◽  
Vol 53 (2) ◽  
pp. 159-180
Author(s):  
V. M. Kyrylych ◽  
O. Z. Slyusarchuk
Keyword(s):  
Boundary Value Problems ◽  
A Priori Estimates ◽  
Hyperbolic Systems ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Mixed Problems ◽  
Priori Estimates ◽  
Smooth Coefficients

Nonlocal boundary value problems for arbitrary order hyperbolic systems with one spatial variable are considered. A priori estimates for general nonlocal mixed problems for systems with smooth and piecewise smooth coefficients are obtained. The correct solvability of such problems is proved.Examples of additional conditions necessity are provided.

scholarly journals Difference methods for solving nonlocal boundary value problems for fractional-order differential convection-diffusion equations with memory effect

2021 ◽  
Vol 21 (1) ◽  
pp. 3-25
Author(s):  
Murat Beshtokov ◽  
◽  
M. Z. KHudalov ◽  
Keyword(s):  
Boundary Value Problems ◽  
Memory Effect ◽  
Fractional Order ◽  
A Priori Estimates ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Uniform Grid ◽  
Integral Sign ◽  
Nonlocal Boundary Value Problems ◽  
Convection Diffusion

In the present paper, in a rectangular domain, we study nonlocal boundary value problems for one-dimensional in space differential equations of convection-diffusion of fractional order with a memory effect, in which the unknown function appears in the differential expression and at the same time appears under the integral sign. The emergence of the integral term in the equation is associated with the need to take into account the dependence of the instantaneous values of the characteristics of the described object on their respective previous values, i.e. the effect of its prehistory on the current state of the system. For the numerical solution of nonlocal boundary value problems, two-layer monotone difference schemes are constructed that approximate these problems on a uniform grid. Estimates of solutions of problems in differential and difference interpretations are derived by the method of energy inequalities. The obtained a priori estimates imply the uniqueness, as well as the continuous and uniform dependence of the solution on the input data of the problems under consideration and, due to the linearity of the problem under consideration, the convergence of the solution of the difference problem to the solution of the corresponding differential problem with the rate $O(h^2+\tau^2)$.

On the well-posedness of boundary value problems for nonclassical differential equations of higher order

2017 ◽  
Vol 10 (03) ◽  
pp. 1750059
Author(s):  
N. R. Pinigina
Keyword(s):  
Boundary Value Problems ◽  
Spectral Parameter ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Fourier Method ◽  
Countable System ◽  
Priori Estimates ◽  
Complex Eigenvalues ◽  
Even Order

This paper investigates a high even-order nonclassical differential equation with a spectral parameter. We proved that this equation has a countable system of nontrivial solutions if spectral parameter is negative. We consider two cases, one where the spectral parameter is equal to eigenvalues and one where the spectral parameter is not equal to eigenvalues. In both cases, we proved the existence of regular solutions of boundary value problems for this equation. To do this, we combined the Fourier method and the method of a priori estimates. Moreover, we found some conditions for unsolvability of boundary value problems. In addition, for adjoint problems, we proved that there is no complex eigenvalues.

A priori estimates of solutions of boundary value problems for two-dimensional systems of singular differential inequalities

2011 ◽  
Vol 18 (1) ◽  
pp. 163-175
Author(s):  
Nino Partsvania
Keyword(s):  
Boundary Value Problems ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Differential Inequalities ◽  
Two Dimensional ◽  
Point Boundary ◽  
Estimates Of Solutions ◽  
Priori Estimates ◽  
Singular Coefficients

Abstract A priori estimates of solutions of two-point boundary value problems for two-dimensional systems of differential inequalities with singular coefficients are established.

Sign in / Sign up

Export Citation Format

Share Document