On the well-posedness of the nonlocal boundary value problem for the differential equation of elliptic type

2018 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Ayman Hamad
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Elliptic Type ◽  
Well Posedness ◽  
Nonlocal Boundary Value Problem

scholarly journals A remark on elliptic differential equations on manifold

2020 ◽  
Vol 99 (3) ◽  
pp. 75-85
Author(s):  
A. Ashyralyev ◽  
◽  
Y. Sozen ◽  
F. Hezenci ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Elliptic Type ◽  
Well Posedness ◽  
Nonlocal Boundary Value Problem ◽  
Elliptic Boundary Value

For elliptic boundary value problems of nonlocal type in Euclidean space, the well posedness has been studied by several authors and it has been well understood. On the other hand, such kind of problems on manifolds have not been studied yet. Present article considers differential equations on smooth closed manifolds. It establishes the well posedness of nonlocal boundary value problems of elliptic type, namely Neumann-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds and also DirichletBitsadze-Samarskii type nonlocal boundary value problem on manifolds, in H¨older spaces. In addition, in various H¨older norms, it establishes new coercivity inequalities for solutions of such elliptic nonlocal type boundary value problems on smooth manifolds.

scholarly journals A note on the nonlocal boundary value problem for a third order partial differential equation

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 801-808 ◽  
Author(s):  
Kh. Belakroum ◽  
A. Ashyralyev ◽  
A. Guezane-Lakoud
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Order Partial Differential Equation ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Partial Differential

The nonlocal boundary-value problem for a third order partial differential equation in a Hilbert space with a self-adjoint positive definite operator is considered. Applying operator approach, the theorem on stability for solution of this nonlocal boundary value problem is established. In applications, the stability estimates for the solution of three nonlocal boundary value problems for third order partial differential equations are obtained.

scholarly journals Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Asker Hanalyev
Keyword(s):  
Differential Equation ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Continuous Functions ◽  
Parabolic Differential Equation ◽  
Well Posedness ◽  
Nonlocal Boundary Value Problem ◽  
Hölder Condition ◽  
Linear Positive Operator

The nonlocal boundary value problem for the parabolic differential equationv'(t)+A(t)v(t)=f(t)  (0≤t≤T),  v(0)=v(λ)+φ,  0<λ≤Tin an arbitrary Banach spaceEwith the dependent linear positive operatorA(t)is investigated. The well-posedness of this problem is established in Banach spacesC0β,γ(Eα-β)of allEα-β-valued continuous functionsφ(t)on[0,T]satisfying a Hölder condition with a weight(t+τ)γ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.

scholarly journals Well-Posedness of the Boundary Value Problem for Parabolic Equations in Difference Analogues of Spaces of Smooth Functions

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
A. Ashyralyev
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Approximate Solutions ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Well Posedness ◽  
Nonlocal Boundary Value Problem ◽  
Smooth Functions ◽  
Accuracy Difference

The first and second orders of accuracy difference schemes for the approximate solutions of the nonlocal boundary value problemv′(t)+Av(t)=f(t)(0≤t≤1),v(0)=v(λ)+μ,0<λ≤1, for differential equation in an arbitrary Banach spaceEwith the strongly positive operatorAare considered. The well-posedness of these difference schemes in difference analogues of spaces of smooth functions is established. In applications, the coercive stability estimates for the solutions of difference schemes for the approximate solutions of the nonlocal boundary value problem for parabolic equation are obtained.

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