Browsing by Author "Kanca, Fatma"
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An Inverse Boundary Value Problem for a Second Order Elliptic Equation in a Rectangle
In this paper the inverse problem of finding a coefficient in a second order elliptic equation is investigated. The conditions for the existence and uniqueness of the classical solution of the problem under consideration are established. Numerical tests using the finitedifference scheme combined with an iteration method is presented and the sensitivity of this scheme with respect to noisy overdetermination data is illustrated.

An inverse coefficient problem for a quasilinear parabolic equation with periodic boundary and integral overdetermination condition
In this paper the inverse problem of finding the timedependent coefficient of heat capacity together with the solution periodic boundary and integral overdetermination conditions is considered. Under some natural regularity and consistency conditions on the input data the existence uniqueness and continuous dependence upon the data of the solution are shown. Some considerations on the numerical solution for this inverse problem are presented with an example. Copyright (c) 2014 John Wiley & Sons Ltd.

An inverse problem for a quasilinear parabolic equation with nonlocal boundary and overdetermination conditions
Authors:Kanca, Fatma; Bağlan, İrem Sakınç
Publisher and Date:(Springer International Publishing Ag, 2014)In this paper the inverse problem of finding the timedependent coefficient of heat capacity together with the solution of heat equation with nonlocal boundary conditions is considered. Under some natural regularity and consistency conditions on the input data the existence uniqueness and continuous dependence upon the data of the solution are shown. Some considerations on the numerical solution for this inverse problem are presented with an example.

Continuous dependence on data for a solution of the quasilinear parabolic equation with a periodic boundary condition
Authors:Kanca, Fatma; Baglan, Irem Sakinc
Publisher and Date:(Springer International Publishing Ag, 2013)In this paper we consider a parabolic equation with a periodic boundary condition and we prove the stability of a solution on the data. We give a numerical example for the stability of the solution on the data.

Determination of a diffusion coefficient in a quasilinear parabolic equation
This paper investigates the inverse problem of finding the timedependent diffusion coefficient in a quasilinear parabolic equation with the nonlocal boundary and integral overdetermination conditions. Under some natural regularity and consistency conditions on the input data the existence uniqueness and continuously dependence upon the data of the solution are shown. Finally some numerical experiments are presented.

Determination of an Unknown Heat Source from Integral Overdetermination Condition
Authors:Baglan, İrem Sakınç; Kanca, Fatma; Mishra, Vishnu Narayan
Publisher and Date:(Springer International Publishing, 2018)In this research we consider a coefficient problem of an inverse problem of a quasilinear parabolic equation with periodic boundary and integral over determination conditions. We prove the existence uniqueness and continuously dependence upon the data of the solution by iteration method. Also we consider numerical solution for this inverse problem using linearization and finite difference method is proved.

Generalized and numerical solution for a quasilinear parabolic equation with nonlocal conditions
In this paper we study the one dimensional mixed problem with nonlocal boundary conditions for the quasilinear parabolic equation. We prove an existence uniqueness of the weak generalized solution and also continuous dependence upon the data of the solution are shown by using the generalized Fourier method. We construct an iteration algorithm for the numerical solution of this problem. We analyze computationally convergence of the iteration algorithm as well as on test example.

An inverse coefficient problem for a quasilinear parabolic equation with nonlocal boundary conditions
In this paper the inverse problem of finding the timedependent coefficient of heat capacity together with the nonlocal boundary conditions is considered. Under some natural regularity and consistency conditions on the input data, the existence, uniqueness and continuous dependence upon the data of the solution are shown. Some considerations on the numerical solution for this inverse problem are presented with an example.

Inverse Coefficient Problem for a SecondOrder Elliptic Equation with Nonlocal Boundary Conditions
In this research article the inverse problem of finding a timedependent coefficient in a secondorder elliptic equation is investigated. The existence and the uniqueness of the classical solution of the problem under consideration are established. Numerical tests using the finitedifference scheme combined with an iteration method are presented and the sensitivity of this scheme with respect to noisy over determination data is illustrated. Copyright (C) 2015 John Wiley & Sons Ltd.

Inverse Coefficient Problem of the Parabolic Equation with Periodic Boundary and Integral Overdetermination Conditions
This paper investigates the inverse problem of finding a timedependent diffusion coefficient in a parabolic equation with the periodic boundary and integral overdetermination conditions. Under some assumption on the data the existence uniqueness and continuous dependence on the data of the solution are shown by using the generalized Fourier method. The accuracy and computational efficiency of the proposed method are verified with the help of the numerical examples.

Numerical solution and distinguishability in time fractional parabolic equation
Authors:Demir, Ali; Kanca, Fatma; Ozbilge, Ebru
Publisher and Date:(Springer International Publishing Ag, 2015)This article deals with the mathematical analysis of the inverse problem of identifying the distinguishability of inputoutput mappings in the linear time fractional inhomogeneous parabolic equation D(t)(alpha)u(x t) = (k(x)u(x))(x) + r(t)F(x t) 0 < alpha = 1 with mixed boundary conditions u(0 t) = psi(0)(t) u(x)(1 t) = psi(1)(t). By defining the inputoutput mappings Phi[center dot] : kappa > C1[0 T] and psi[center dot] : kappa > C[0 T] the inverse problem is reduced to the problem of their ...

The inverse problem of the heat equation with periodic boundary and integral overdetermination conditions
In this paper the inverse problem of finding the timedependent coefficient of heat capacity together with the solution of a heat equation with periodic boundary and integral overdetermination conditions is considered. The conditions for the existence and uniqueness of a classical solution of the problem under consideration are established. A numerical example using the CrankNicolson finitedifference scheme combined with the iteration method is presented.

Twodimensional inverse quasilinear parabolic problem with periodic boundary condition
In this study we consider a coefficient problem of a quasilinear twodimensional parabolic inverse problem with periodic boundary and integral over determination conditions. We prove the existence uniqueness and continuously dependence upon the data of the solution by iteration method. Also we consider numerical solution for this inverse problem by using linearization and the implicit finitedifference scheme.

Weak generalized and numerical solution for a quasilinear pseudoparabolic equation with nonlocal boundary condition
Authors:Bağlan, İrem Sakınç; Kanca, Fatma
Publisher and Date:(Springer International Publishing, 2014)This paper investigates the one dimensional mixed problem with nonlocal boundary conditions for the quasilinear parabolic equation. Under some natural regularity and consistency conditions on the input data the existence uniqueness convergence of the weak generalized solution and also continuous dependence upon the data of the solution are shown by using the generalized Fourier method. We construct an iteration algorithm for the numerical solution of this problem.

Untitled
Authors:Özbilge, Ebru; Demir, Ali; Kanca, Fatma; Özbilge, Emre
Publisher and Date:(Natural Sciences Publishing USA, 2016)This article deals with the mathematical analysis of the inverse problem of identifying the distinguishability of inputoutput mappings in the linear time fractional inhomogeneous parabolic equation Dt α u(x, t)=(k(x)ux)x+r(t)F(x, t) 0 < α ≤ 1, with Dirichlet boundary conditions u(0, t) = Ψ0(t), u(1, t) = Ψ1(t). By defining the inputoutput mappings Φ[·]: K →C1[0,T ] and Ψ[·]: K → C1[0,T] the inverse problem is reduced to the problem of their invertibility. Hence, the main purpose of this study ...