scholarly journals Well-posedness of boundary value problems for reverse parabolic equation with integral condition

2018 ◽  
Vol 1 (1) ◽  
pp. 11-21
Author(s):  
Charyyar Ashyralyyev
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problems ◽  
Parabolic Problem ◽  
Boundary Value ◽  
Integral Condition ◽  
Stability Estimates ◽  
Well Posedness ◽  
Holder Space ◽  
Hölder Space ◽  
Coercive Stability

AbstractReverse parabolic equation with integral condition is considered. Well-posedness of reverse parabolic problem in the Hölder space is proved. Coercive stability estimates for solution of three boundary value problems (BVPs) to reverse parabolic equation with integral condition are established.

scholarly journals Boundary-value problems in a layer for evolutionary pseudo-differential equations with integral conditions

2018 ◽  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Condition ◽  
Well Posedness ◽  
Integral Conditions ◽  
Pseudo Differential Equation ◽  
Necessary And Sufficient ◽  
Well Posed

Boundary-value problems for evolutionary pseudo-differential equations with an integral condition are studied. Necessary and sufficient conditions of well-posedness are obtained for these problems in the Schwartz spaces. Existence of a well-posed boundary-value problem is proved for each evolutionary pseudo-differential equation.

scholarly journals Parabolic time dependent source identification problem with involution and Neumann condition

2021 ◽  
Vol 102 (2) ◽  
pp. 5-15
Author(s):  
A. Ashyralyev ◽  
◽  
A.S. Erdogan ◽  
◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Parabolic Equation ◽  
Source Identification ◽  
Parabolic Problem ◽  
Identification Problem ◽  
Time Dependent ◽  
Neumann Condition ◽  
Stability Estimates ◽  
Well Posedness

A time dependent source identification problem for parabolic equation with involution and Neumann condition is studied. The well-posedness theorem on the differential equation of the source identification parabolic problem is established. The stable difference scheme for the approximate solution of this problem and its stability estimates are presented. Numerical results are given.

Well-posedness of a nonlocal boundary value difference elliptic problem

2019 ◽  
Vol 14 (5) ◽  
pp. 507
Author(s):  
Allaberen Ashyralyev ◽  
Ayman Hamad
Keyword(s):  
Difference Scheme ◽  
Numerical Solution ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Well Posedness ◽  
The Difference ◽  
The Stability ◽  
Coercive Stability ◽  
Second Order Of Approximation

The second order of approximation two-step difference scheme for the numerical solution of a nonlocal boundary value problem for the elliptic differential equation [see formula in PDF] in an arbitrary Banach space E with the positive operator A is presented. The well-posedness of the difference scheme in Banach spaces is established. In applications, the stability, almost coercive stability and coercive stability estimates in maximum norm in one variable for the solutions of difference schemes for numerical solution of two type elliptic problems are obtained.

On Solvability and Well-Posedness of Boundary Value Problems for Nonlinear Hyperbolic Equations of the Fourth Order

2008 ◽  
Vol 15 (3) ◽  
pp. 555-569
Author(s):  
Tariel Kiguradze
Keyword(s):  
Hyperbolic Equation ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Hyperbolic Equation ◽  
Well Posedness ◽  
Nonlinear Hyperbolic Equations ◽  
Right Hand

Abstract In the rectangle Ω = [0, a] × [0, b] the nonlinear hyperbolic equation 𝑢(2,2) = 𝑓(𝑥, 𝑦, 𝑢) with the continuous right-hand side 𝑓 : Ω × ℝ → ℝ is considered. Unimprovable in a sense sufficient conditions of solvability of Dirichlet, Dirichlet–Nicoletti and Nicoletti boundary value problems are established.

Solution of the nonregular problem for a parabolic equation with the time derivative in the boundary condition

2021 ◽  
pp. 1-35
Author(s):  
Galina Bizhanova
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Parabolic Equation ◽  
Small Parameter ◽  
Unique Solvability ◽  
Time Derivative ◽  
Holder Space ◽  
Hölder Space ◽  
Space Solution ◽  
Unperturbed Problem

There is studied the Hölder space solution u ε of the problem for parabolic equation with the time derivative ε ∂ t u ε | Σ in the boundary condition, where ε > 0 is a small parameter. The unique solvability of the perturbed problem and estimates of it’s solution are obtained. The convergence of u ε as ε → 0 to the solution of the unperturbed problem is proved. Boundary layer is not appeared.

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