scholarly journals The Galerkin Method for Fourth-Order Equation of the Moore–Gibson–Thompson Type with Integral Condition

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Ahlem Mesloub ◽  
Abderrahmane Zara ◽  
Fatiha Mesloub ◽  
Bahri-Belkacem Cherif ◽  
Mohamed Abdalla
Keyword(s):  
Galerkin Method ◽  
Fourth Order ◽  
Nonlocal Problem ◽  
Integral Condition ◽  
Order Equation ◽  
Galerkin’S Method ◽  
Fourth Order Equation ◽  
Galerkin's Method ◽  
The Galerkin Method ◽  
The Given

In this manuscript, we consider the fourth order of the Moore–Gibson–Thompson equation by using Galerkin’s method to prove the solvability of the given nonlocal problem.

scholarly journals A NONLOCAL PROBLEM WITH INTEGRAL CONDITION FOR A FOURTH ORDER EQUATION

2017 ◽  
Vol 22 (3-4) ◽  
pp. 32-50
Author(s):  
V. B. Dmitriev
Keyword(s):  
Fourth Order ◽  
Regularization Method ◽  
Nonlocal Problem ◽  
Integral Condition ◽  
Initial Boundary ◽  
Order Equation ◽  
Integral Conditions ◽  
Boundary Problems ◽  
Fourth Order Equation ◽  
Apriori Estimates

In this paper we consider initial-boundary problems with integral conditions for certain fourth order equation. Unique solvability of posed problems is proved. The proof is based on apriori estimates, regularization method, auxiliary problems method, embedding theorems.

scholarly journals On a nonlocal boundary value problem for the equation fourth-order in partial derivatives

2021 ◽  
pp. 16-23
Author(s):  
О.Ш. Киличов
Keyword(s):  
Boundary Value Problem ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Problem ◽  
Order Equation ◽  
Nonlocal Boundary Value Problem ◽  
Fourth Order Equation ◽  
Uniqueness Of A Solution

В данной статье изучается нелокальная задача для уравнения четвертого порядка в которой доказывается существование и единственность решения этой задачи. Решение построено явно в виде ряда Фурье, обоснованы абсолютная и равномерная сходимость полученного ряда и возможность почленного дифференцирования решения по всем переменным. Установлен критерий однозначной разрешимости поставленной краевой задачи. In this article, we study a nonlocal problem for a fourth-order equation in which the existence and uniqueness of a solution to this problem is proved. The solution is constructed explicitly in the form of a Fourier series; the absolute and uniform convergence of the obtained series and the possibility of term-by-term differentiation of the solution with respect to all variables are substantiated. A criterion for the unique solvability of the stated boundary value problem is established.

scholarly journals NONLOCAL PROBLEM WITH INTEGRAL CONDITION FOR A FOURTH ORDER EQUATION

2017 ◽  
Vol 20 (10) ◽  
pp. 26-37
Author(s):  
N.V. Beilina
Keyword(s):  
Differential Equation ◽  
Nonlocal Problem ◽  
Convergent Subsequence ◽  
Integral Condition ◽  
Approximate Solutions ◽  
Generalized Solution ◽  
Order Equation ◽  
Order Partial Differential Equation ◽  
Fourth Order Equation ◽  
Apriori Estimates

In this paper, we consider a nonlocal problem with integral condition with respect to spacial variable for a forth order partial differential equation. The conditions on the data for unique solvability of the problem in Sobolev space are determined. Proving of uniqueness of generalized solution is based on acquired apriori estimates. To prove the solvability we use a following scheme: sequence of approximate solutions using Galerkin procedure is built, apriory estimates that allow to extract from it a convergent subsequence are received, on the final stage it is shown that the limit of subsequence is the required generalized solution.

A Geometrical Solution for the Inverse Kinematics of Three Revolute Manipulators

1993 ◽  
Author(s):  
Eugene F. Fichter
Keyword(s):  
Fourth Order ◽  
Inverse Kinematics ◽  
Solution Procedure ◽  
Order Equation ◽  
Algebraic Solution ◽  
Computer Implementation ◽  
Third Order ◽  
Fourth Order Equation ◽  
Inverse Kinematics Problem

Abstract Points of intersection of a circle and a torus are used to find a solution to the inverse kinematics problem for a three revolute manipulator. Both geometrical and algebraic solution procedures are discussed. The algebraic procedure begins with a third order equation instead of the usual fourth order equation. Since the procedure is basically geometrical it lends itself to a computer implementation which graphically displays each steps in the solution procedure. The potential of this approach for both design and pedagogy is discussed.

26.—The Strong Limit-2 Case of Fourth-order Differential Equations

1974 ◽  
Vol 71 (4) ◽  
pp. 297-304
Author(s):  
V. Krishna Kumar
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Order Equation ◽  
Complex Numbers ◽  
Strong Limit ◽  
Fourth Order Equation ◽  
Linearly Independent ◽  
Image Position ◽  
Adjoint Operators ◽  
Bounded Below

SynopsisThe fourth-order equation considered isConditions are given on the coefficients r, p and q which ensure that this differential equation (*) is in the strong limit-2 case at ∞, i.e. is limit-2 at ∞. This implies that (*) has exactly two linearly independent solutions which are in the integrable-square space ℒ2(0, ∞) for all complex numbers λ with im [λ] ≠ 0. Additionally the conditions imply that self-adjoint operators generated by M[·] in ℒ2(0, ∞) are semi-bounded below. The results obtained are applied to the case when the coefficients r, p and q are powers of x ∈ [0, ∞).

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