An estimate concerning the difference between minimizer and boundary value in some polyconvex problems

2022 ◽  
Vol 215 ◽  
pp. 112635
Author(s):  
Renato Colucci ◽  
Francesco Leonetti ◽  
Giulia Treu
Keyword(s):  
Boundary Value ◽  
The Difference

scholarly journals On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Ozgur Yildirim ◽  
Meltem Uzun
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Order Of Accuracy ◽  
Definite Operator ◽  
The Difference

This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented.

scholarly journals Global theorem of existence and uniqueness of the firstboundary value problem for nonlinear integrodifferential equations ofparabolic type

2017 ◽  
Vol 21 (3) ◽  
pp. 64-72
Author(s):  
O.P. Filatov
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Parabolic Type ◽  
Current Application ◽  
Real Model ◽  
Fuel Tanks ◽  
The Difference ◽  
The Right ◽  
A Current

Global theorem of existence and uniqueness of solution of the first boundary value problem for nonlinear integrodifferential equation of parabolic type is proved. If the right-hand side of the equation is integrally bounded, then we have estimate of the norm of the difference of two solutions, which implies continuous dependence of solution on the initial function and uniqueness of so- lution of the first boundary value problem. The problem under consideration generalizes the real model for measuring the level of incompressible fluid in the fuel tanks missiles. Therefore, such problem have a current application.

scholarly journals Boundary-Value Problems for Differential-Difference Equations with Incommeasurable Shifts of Arguments Reducible to Nonlocal Problems

2019 ◽  
Vol 65 (4) ◽  
pp. 613-622
Author(s):  
E. P. Ivanova
Keyword(s):  
Boundary Value Problems ◽  
Difference Equations ◽  
Original Problem ◽  
Difference Operator ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Nonlocal Problems ◽  
Higher Order Terms ◽  
The Difference

We consider boundary-value problems for differential-difference equations containing incommeasurable shifts of arguments in higher-order terms. We prove that in the case of finite orbits of boundary points generated by the set of shifts of the difference operator, the original problem is reduced to the boundary-value problem for differential equation with nonlocal boundary conditions.

A High-Order Difference Scheme for a Nonlocal Boundary-Value Problem for the Heat Equation

2001 ◽  
Vol 1 (4) ◽  
pp. 398-414 ◽  
Author(s):  
Zhi-Zhong Sun
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
High Order ◽  
Order Difference ◽  
Local Boundary ◽  
Non Local ◽  
The Difference ◽  
Boundary Equations

Abstract This paper is concerned with a high order difference scheme for a non- local boundary-value problem of parabolic equation. The integrals in the boundary equations are approximated by the composite Simpson rule. The unconditional solv- ability and L_∞ convergence of the difference scheme is proved by the energy method. The convergence rate of the difference scheme is second order in time and fourth order in space. Some numerical examples are provided to illustrate the convergence.

scholarly journals An iteration method for the determination of an unknown boundary condition in a parabolic initial-boundary value problem

1989 ◽  
Vol 32 (1) ◽  
pp. 59-71 ◽  
Author(s):  
Michael Pilant ◽  
William Rundell
Keyword(s):  
Boundary Value Problem ◽  
Heat Conduction Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Fourth Power ◽  
Unknown Boundary ◽  
The Difference ◽  
Image Position ◽  
Initial Boundary Value

Consider the initial boundary value problemIn the context of the heat conduction problem, this models the case where the heat flux across the ends at the rod is a function of the temperature. If the heat exchange between the rod and its surroundings is purely by convection, then one commonly assumes that f is a linear function of the difference in temperatures between the ends of the rod and that of the surroundings, (Newton's law of cooling). For the case of purely radiative transfer of energy a fourth power law for the function f is usual, (Stefan's law).

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