scholarly journals Existence and uniqueness results for an inverse problem for a semilinear equation with final overdetermination

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 847-858 ◽  
Author(s):  
Ali Sazaklioglu ◽  
Abdullah Erdogan ◽  
Allaberen Ashyralyev
Keyword(s):  
Banach Space ◽  
Inverse Problem ◽  
Difference Scheme ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Order Of Accuracy ◽  
First Order ◽  
Existence And Uniqueness Results ◽  
Semilinear Equation ◽  
Uniqueness Results

In the present paper, unique solvability of a source identification inverse problem for a semilinear equation with a final overdetermination in a Banach space is investigated. Moreover, the first order of accuracy Rothe difference scheme is presented for numerically solving this problem. The existence and uniqueness result for this difference scheme is given. The efficiency of the proposed method is evaluated by means of computational experiments.

Existence and uniqueness results for an inverse problem for semilinear parabolic equations

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1057-1064 ◽  
Author(s):  
Ali Sazaklioglu ◽  
Allaberen Ashyralyev ◽  
Abdullah Erdogan
Keyword(s):  
Inverse Problem ◽  
Difference Scheme ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Semilinear Parabolic Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Accuracy Difference ◽  
Integral Overdetermination ◽  
Semilinear Parabolic

In the present study, unique solvability of an inverse problem governed by semilinear parabolic equations with an integral overdetermination is investigated. Furthermore, for the approximate solution of this problem a first order of accuracy difference scheme is constructed. Existence and uniqueness results for the solution of this difference scheme are established. Considering a particular example, some numerical results are discussed.

scholarly journals Weak solvability of the unconditionally stable difference scheme for the coupled sine-Gordon system

2020 ◽  
Vol 25 (6) ◽  
pp. 997-1014
Author(s):  
Ozgur Yildirim ◽  
Meltem Uzun
Keyword(s):  
Difference Scheme ◽  
Numerical Method ◽  
Existence And Uniqueness ◽  
Numerical Experiments ◽  
Finite Difference Schemes ◽  
Order Of Accuracy ◽  
Unconditionally Stable ◽  
First Order ◽  
The Difference ◽  
Weak Solvability

In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability.We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method.

Existence and uniqueness results for a class of elliptic equations with exponential nonlinearity

2005 ◽  
Vol 135 (5) ◽  
pp. 959-983
Author(s):  
Kwangseok Choe
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Existence Results ◽  
Implicit Function ◽  
Exponential Nonlinearity ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Semilinear Elliptic

We establish existence results for a class of semilinear elliptic equations with exponential nonlinearity by studying a suitable eigenvalue problem. We also establish a uniqueness result for those equations by making use of the implicit function theorem.

Existence and uniqueness results for a class of elliptic equations with exponential nonlinearity

2005 ◽  
Vol 135 (5) ◽  
pp. 959-983 ◽  
Author(s):  
Kwangseok Choe
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Existence Results ◽  
Implicit Function ◽  
Exponential Nonlinearity ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Semilinear Elliptic

We establish existence results for a class of semilinear elliptic equations with exponential nonlinearity by studying a suitable eigenvalue problem. We also establish a uniqueness result for those equations by making use of the implicit function theorem.

scholarly journals Existence results for boundary value problems of arbitrary order integrodifferential equations in Banach spaces

2013 ◽  
Vol 21 (2) ◽  
pp. 155-171 ◽  
Author(s):  
K. Karthikeyan ◽  
Bashir Ahmad
Keyword(s):  
Banach Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Arbitrary Order ◽  
Boundary Value ◽  
Existence Results ◽  
Integrodifferential Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Caputo’S Derivative

Abstract We study a boundary value problem of fractional integrodifferential equations involving Caputo's derivative of order α ∈ (n-1,n) in a Banach space. Existence and uniqueness results for the problem are established by means of the Hölder's inequality together with some standard fixed point theorems

scholarly journals Homotopy Analysis Method for the First Order Fuzzy Volterra-Fredholm Integro-differential Equations

2018 ◽  
Vol 11 (3) ◽  
pp. 857 ◽  
Author(s):  
Ahmed A. Hamoud ◽  
Kirtiwant P. Ghadle
Keyword(s):  
Differential Equation ◽  
Homotopy Analysis Method ◽  
Existence And Uniqueness ◽  
Analysis Method ◽  
First Order ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Homotopy Analysis ◽  
Fuzzy Solution ◽  
Parametric Case

A fuzzy Volterra-Fredholm integro-differential equation (FVFIDE) in a parametric case is converted to its related crisp case.  We use homotopy analysis method to find the approximate solution of this system and hence obtain an approximation for the fuzzy solution of the  FVFIDE. This paper discusses existence and uniqueness results and convergence of the proposed method.

scholarly journals Existence and uniqueness results for the first-order non-linear impulsive integro-differential equations with two-point boundary conditions

2021 ◽  
Vol 102 (2) ◽  
pp. 74-83
Author(s):  
M.J. Mardanov ◽  
◽  
R.S. Mammadov ◽  
S.Yu. Gasimov ◽  
Ya.A. Sharifov ◽  
...  
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Contraction Mapping Principle ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
The Green Function

The article discusses the existence and uniqueness of solutions for a system of nonlinear integro-differential equations of the first order with two-point boundary conditions. The Green function is constructed, and the problem under consideration is reduced to equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach contraction mapping principle. Schaefer’s fixed point theorem is used to prove the existence of solutions.

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