Browsing by Author "Kanca, Fatma"

Now showing 1 - 14 of 14

Citation Count: 1
Continuous dependence on data for a solution of the quasilinear parabolic equation with a periodic boundary condition
(Springer International Publishing Ag, 2013) Kanca, Fatma; Baglan, Irem Sakinc; Kanca, Fatma
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.
Citation Count: 2
Determination of a diffusion coefficient in a quasilinear parabolic equation
(De Gruyter Open Ltd, 2017) Kanca, Fatma
This paper investigates the inverse problem of finding the time-dependent 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.
Citation Count: 5
Determination of an Unknown Heat Source from Integral Overdetermination Condition
(Springer International Publishing, 2018) Baglan, İrem Sakınç; Kanca, Fatma; Mishra, Vishnu Narayan
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.
Citation Count: 0
Generalized and numerical solution for a quasilinear parabolic equation with nonlocal conditions
(Univ Babes-Bolyai, 2015) Kanca, Fatma; Baglan, Irem Sakinc
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.
Citation Count: 14
An Inverse Boundary Value Problem for a Second Order Elliptic Equation in a Rectangle
(Vilnius Gediminas Tech Univ, 2014) Mehraliyev, Yashar T.; Kanca, Fatma
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 finite-difference scheme combined with an iteration method is presented and the sensitivity of this scheme with respect to noisy overdetermination data is illustrated.
Citation Count: 5
An inverse coefficient problem for a quasilinear parabolic equation with nonlocal boundary conditions
(Springer International Publishing Ag, 2013) Kanca, Fatma; Bağlan, İrem
In this paper the inverse problem of finding the time-dependent 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.
Citation Count: 8
An inverse coefficient problem for a quasilinear parabolic equation with periodic boundary and integral overdetermination condition
(Wiley-Blackwell, 2015) Bağlan, İrem Sakınç; Kanca, Fatma
In this paper the inverse problem of finding the time-dependent 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.
Citation Count: 3
Inverse Coefficient Problem for a Second-Order Elliptic Equation with Nonlocal Boundary Conditions
(Wiley, 2016) Kanca, Fatma
In this research article the inverse problem of finding a time-dependent coefficient in a second-order elliptic equation is investigated. The existence and the uniqueness of the classical solution of the problem under consideration are established. Numerical tests using the finite-difference 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.
Citation Count: 9
Inverse Coefficient Problem of the Parabolic Equation with Periodic Boundary and Integral Overdetermination Conditions
(Hindawi Publishing Corporation, 2013) Kanca, Fatma
This paper investigates the inverse problem of finding a time-dependent 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.
Citation Count: 2
An inverse problem for a quasilinear parabolic equation with nonlocal boundary and overdetermination conditions
(Springer International Publishing Ag, 2014) Kanca, Fatma; Bağlan, İrem Sakınç
In this paper the inverse problem of finding the time-dependent 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.
Citation Count: 8
The inverse problem of the heat equation with periodic boundary and integral overdetermination conditions
(Springer International Publishing Ag, 2013) Kanca, Fatma
In this paper the inverse problem of finding the time-dependent 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 Crank-Nicolson finite-difference scheme combined with the iteration method is presented.
Citation Count: 10
Numerical solution and distinguishability in time fractional parabolic equation
(Springer International Publishing Ag, 2015) Demir, Ali; Kanca, Fatma; Ozbilge, Ebru
This article deals with the mathematical analysis of the inverse problem of identifying the distinguishability of input-output 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 input-output mappings Phi[center dot] : kappa -> C-1[0 T] and psi[center dot] : kappa -> C[0 T] the inverse problem is reduced to the problem of their invertibility. Hence the main purpose of this study is to investigate the distinguishability of the input-output mappings Phi[center dot] and psi[center dot]. Moreover the measured output data f (t) and h(t) can be determined analytically by a series representation which implies that the input-output mappings Phi[center dot] : kappa -> C-1[0 T] and psi[center dot] : kappa -> C[0 T] can be described explicitly where Phi[r] = k(x)u(x)(x t
Citation Count: 7
Two-dimensional inverse quasilinear parabolic problem with periodic boundary condition
(Taylor & Francis Ltd, 2019) Baglan, İrem Sakınç; Kanca, Fatma
In this study we consider a coefficient problem of a quasi-linear two-dimensional 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 finite-difference scheme.
Citation Count: 1
Weak generalized and numerical solution for a quasilinear pseudo-parabolic equation with nonlocal boundary condition
(Springer International Publishing, 2014) Bağlan, İrem Sakınç; Kanca, Fatma
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.