Browsing by Author "Demir, Ali"

Now showing 1 - 14 of 14

Citation - WoS: 1
Citation - Scopus: 1
Analysis for the Identification of an Unknown Diffusion Coefficient Via Semigroup Approach
(Wiley, 2009) Demir, Ali; Özbilge Kahveci, Ebru
This paper presents a semigroup approach for the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient k(u(x)) in the inhomogenenous quasi-linear parabolic equation u(t)(x, t) = (k(u(x))u(x)(x, t))(x) + F(u) with the Dirichlet boundary conditions u(0, t)=psi(0),u(1, t)=psi(1) and source function F(u). The main purpose of this paper is to investigate the distinguishability of the input-output mappings Phi[.] : K -> C-1[0, T], psi[.]: K -> C-1[0,T] via sernigroup theory. Copyright (C) 2009 John Wiley & Sons, Ltd.
Citation - WoS: 12
Citation - Scopus: 14
Analysis of a Semigroup Approach in the Inverse Problem of Identifying an Unknown Coefficient
(John Wiley & Sons Ltd, 2008) Demir, Ali; Özbilge Kahveci, Ebru
This article presents a semigroup approach to the mathematical analysis of the inverse coefficient problems of identifying file Unknown coefficient k(u(x)) in file quasi-linear parabolic equation u(t)(x,t) = (k(u(x))u(x)(x,t))(x) +F(x,t), with Dirichlet boundary conditions u(0,t)=psi(0), u(l,t) = psi(1) and funclion F(x,t). The main purpose of this paper is to investigate the distinguishability of the input-out mappings phi[center dot]:k -> C-1[0,T], psi[center dot]:K -> C-1[0,T] via semigroup theory. Copyright (C) 2008 John Wiley & Sons, Ltd.
Citation - WoS: 4
Citation - Scopus: 4
Analysis of a Semigroup Approach in the Inverse Problem of Identifying an Unknown Parameters
(Elsevier Science Inc, 2011) Özbilge Kahveci, Ebru; Demir, Ali
This article presents a semigroup approach to the mathematical analysis of the inverse parameter problems of identifying the unknown parameters p(t) and q in the linear parabolic equation u(t)(x, t) = u(xx) + qu(x)(x, t) + p(t)u(x, t), with Dirichlet boundary conditions u(0, t) = psi(0), u(1, t) = psi(1). The main purpose of this paper is to investigate the distinguishability of the input-output mapping Phi[.] : P -> H-1,H- 2 [0, T], via semigroup theory. In this paper, it is shown that if the nullspace of the semigroup T(t) consists of only zero function, then the input-output mapping Phi[.] has the distinguishability property. It is also shown that the types of the boundary conditions and the region on which the problem is defined play an important role in the distinguishability property of the mapping. Moreover, under the light of the measured output data u(x)(0, t) = f(t) the unknown parameter p(t) at (x, t) = (0, 0) and the unknown coefficient q are determined via the input data. Furthermore, it is shown that measured output data f(t) can be determined analytically by an integral representation. Hence the input-output mapping Phi[.] : P -> H-1,H-2 [0, T] is given explicitly interms of the semigroup. (C) 2011 Elsevier Inc. All rights reserved.
Citation - WoS: 11
Citation - Scopus: 10
Analysis of the Inverse Problem in a Time Fractional Parabolic Equation With Mixed Boundary Conditions
(Springer, 2014) Özbilge Kahveci, Ebru; Demir, Ali
This article deals with the mathematical analysis of the inverse coefficient problem of identifying the unknown coefficient k(x) in the linear time fractional parabolic equation D-t(alpha) u(x, t) = (k(x)u(x))(x), 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[.] : kappa -> C-1[0, T] and psi[.] : 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[.] and Phi[.]. This work shows that the input-output mappings Phi[.] and Phi[.] have the distinguishability property. Moreover, the value k(0) of the unknown diffusion coefficient k(x) at x = 0 can be determined explicitly by making use of measured output data (boundary observation) k(0) ux(0, t) = f (t), which brings greater restriction on the set of admissible coefficients. It is also shown that 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[.] : kappa -> C1[0, T] and Phi[.] : kappa -> C[0, T] can be described explicitly.
Citation - Scopus: 3
Determination of the Unknown Source Function in Time Fractional Parabolic Equation With Dirichlet Boundary Conditions
(Natural Sciences Publishing USA, 2016) Ozbilge E.; Demir, Ali; Kanca F.
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 Dt ? u(x, t)=(k(x)ux)x+r(t)F(x, t) 0 < ? ? 1, with Dirichlet boundary conditions u(0, t) = ?0(t), u(1, t) = ?1(t). By defining the input-output mappings ?[·]: K ?C1[0,T ] and ?[·]: K ? C1[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 ?[·] and ?[·]. 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 ? [·] :K ? C1[0,T] and ?[·] :K ? C1[0,T] can be described explicitly. © 2016 NSP Natural Sciences Publishing Cor.
Citation - WoS: 1
Citation - Scopus: 1
Distinguishability of a Source Function in a Time Fractional Inhomogeneous Parabolic Equation With Robin Boundary Condition
(Hacettepe Univ, Fac Sci, 2018) Özbilge Kahveci, Ebru; Demir, Ali
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) + F(x, t) 0 < alpha <= 1, with Robin boundary conditions u(0, t) = psi(0)(t), u(x)(1,t ) = gamma(u(1, t) - psi(1)(t)). By defining the input-output mappings Phi[.] : K -> C-1[0, T] and Psi[.] : K -> 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[.] and Psi[.]. 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[.] : K -> C-1[0, T] and Psi[.] : K -> C[0, T] can be described explicitly.
Identification of an Unknown Coefficient Approximately
(2009) Ozbilge E.; Demir, Ali
This article presents a semigroup approach to the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient a(x,t) approximately in the equation Ut(x,t) = Uxx(x,t) + a(x,t)u(x,t), with Dirichlet boundary conditions u(0,t) =?0, u(l,t) = ?1 It is shown that the unknown coefficient a(x,t) can be approximately determined via semigroup approach. © 2009 American Institute of Physics.
Citation - WoS: 9
Citation - Scopus: 9
Identification of the Unknown Boundary Condition in a Linear Parabolic Equation
(Springer International Publishing Ag, 2013) Demir, Ali; Özbilge Kahveci, Ebru
In this article, a semigroup approach is presented for the mathematical analysis of the inverse problems of identifying the unknown boundary condition in a linear parabolic equation with Dirichlet boundary conditions , by making use of the over measured data and separately.
Citation - WoS: 2
Citation - Scopus: 4
Identification of the Unknown Diffusion Coefficient in a Linear Parabolic Equation Via Semigroup Approach
(Springer International Publishing Ag, 2014) Özbilge Kahveci, Ebru; Demir, Ali
This article presents a semigroup approach to the mathematical analysis of the inverse parameter problems of identifying the unknown parameters p(t) and q in the linear parabolic equation u(t)(x,t) = u(xx) + qu(x)(x, t) + p(t) u(x,t), with mixed boundary conditions u(x)(0, t) = psi(0), k(1) u(1, t) = psi(1). The main purpose of this paper is to investigate the distinguishability of the input-output mapping Phi[.] : P -> H-1,H-2[0, T], via semigroup theory. In this paper, it is shown that if the nullspace of the semigroup T(t) consists of only the zero function, then the input-output mapping Phi[.] has the distinguishability property. It is also shown that both types of boundary conditions and also the region in which the problem is defined play an important role in the distinguishability property of the input-output mapping. Moreover, the input data can be used to determine the unknown parameter p(t) at (x, t) = (0, 0) and also the unknown coefficient q. Furthermore, it is shown that measured output data f(t) can be determined analytically by an integral representation. Hence the input-output mapping Phi[.] : P -> H-1,H-2[0, T] is given explicitly in terms of the semigroup.
Citation - WoS: 7
Citation - Scopus: 7
Identification of Unknown Coefficient in Time Fractional Parabolic Equation With Mixed Boundary Conditions Via Semigroup Approach
(Dynamic Publishers, Inc, 2015) Özbilge Kahveci, Ebru; Demir, Ali
This article presents a semigroup approach for the mathematical analysis of the inverse coefficient problem of identifying the unknown coefficient k(x) in the linear time fractional parabolic equation D(t)(alpha)u(x, t) = (k(x)u(x))(x), 0 < alpha <= 1, with mixed boundary conditions u(0, t) = psi(0)(t) u(x)(1, t) = psi(1)(t). Our aim is the investigation of the distinguishability of the input-output mapping Phi[center dot] : kappa -> C[0, T], via semigroup theory. This work shows that if the null space of the semigroup T-alpha,T-alpha(t) consists of only zero function, then the input-output mapping Phi[center dot] has distinguishability property. Also, the value k(0) of the unknown function k(x) is determined explicitly. In addition to these the boundary observation f(t) can be shown as an integral representation. This also implies that the mapping Phi[center dot] : kappa -> C[0, T] can be described in terms of the semigroup.
Citation - WoS: 12
Citation - Scopus: 19
Inverse Problem for a Time-Fractional Parabolic Equation
(Springer, 2015) Özbilge Kahveci, Ebru; Demir, Ali
This article deals with the mathematical analysis of the inverse coefficient problem of identifying the unknown coefficient k(x) in the linear time-fractional parabolic equation D-t(alpha) u(x,t) = (k(x)u(x))(x) + qu(x)(x,t) + p(t)u(x,t), 0 <= alpha <= 1, with mixed boundary conditions k(0)u(x)(0,t) = psi(0)(t), u(1,t) = psi(1)(t). By defining the input-output mappings Phi[.] : K -> C[0, T] and psi [.] : K -> C-1[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[.] and psi[.]. This work shows that the input-output mappings Phi[.] and psi[.] have distinguishability property. Moreover, the value k(1) of the unknown diffusion coefficient k(x) at x = 1 can be determined explicitly by making use of measured output data (boundary observation) k(1)u(x)(1, t) = h(t), which brings about a greater restriction on the set of admissible coefficients. It is also shown that the measured output data f (t) and h(t) can be determined analytically by a series representation. Hence the input-output mappings Phi[.] : K -> C[0, T] and psi [.] : K -> C-1[0, T] can be described explicitly, where Phi[k] = u(x,t;k)|(x=0) and psi[k] = k(x)u(x)(x,t;k)vertical bar(x=1).
Citation - WoS: 11
Citation - Scopus: 10
Numerical Solution and Distinguishability in Time Fractional Parabolic Equation
(Springeropen, 2015) Demir, Ali; Kanca, Fatma; Özbilge Kahveci, 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; r)vertical bar(x= 0) and psi[r] = u(x, t; r)vertical bar(x= 1). Also, numerical tests using finite difference scheme combined with an iterative method are presented.
Citation - WoS: 9
Citation - Scopus: 10
Semigroup Approach for Identification of the Unknown Diffusion Coefficient in a Linear Parabolic Equation With Mixed Output Data
(Springer International Publishing Ag, 2013) Özbilge Kahveci, Ebru; Demir, Ali
This article presents a semigroup approach for the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient k(x) in the linear parabolic equation u(t)(x,t) = (k(x)u(x)(x,t))(x) with mixed boundary conditions k(0)u(x)(0,t) = psi(0), u(1, t) = psi(1). The aim of this paper is to investigate the distinguishability of the input-output mappings Phi[.]: kappa -> H-1,H-2[0,T], Psi[.] : kappa -> H-1,H-2[0,T] via semigroup theory. In this paper, we show that if the null space of the semigroup T(t) consists of only zero function, then the input-output mappings Phi[.] and Psi[.] have the distinguishability property. It is shown that the types of the boundary conditions and the region on which the problem is defined have a significant impact on the distinguishability property of these mappings. Moreover, in the light of measured output data (boundary observations) f(t) := u(0,t) or/and h(t) := k(1)u(x)(1, t), the values k(0) and k(1) of the unknown diffusion coefficient k(x) at x = 0 and x = 1, respectively, can be determined explicitly. In addition to these, the values k'(0) and k'(1) of the unknown coefficient k(x) at x = 0 and x = 1, respectively, are also determined via the input data. Furthermore, it is shown that measured output data f (t) and h(t) can be determined analytically by an integral representation. Hence the input-output mappings Phi[.] : kappa -> H-1,H-2[0,T], Psi[.] : kappa -> H-1,H-2[0,T] are given explicitly in terms of the semigroup.
Citation - WoS: 15
Citation - Scopus: 17
Semigroup Approach for Identification of the Unknown Diffusion Coefficient in a Quasi-Linear Parabolic Equation
(John Wiley & Sons Ltd, 2007) Demir, Ali; Ozbilge, Ebru
This article presents a semigroup approach for the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient k (u (x, t)) in the quasi-linear parabolic equation u(t) (x, t) = (k(u (x, t))u, (x, t))x, with Dirichlet boundary conditions u(0, t) = psi(0), u(1, t) = psi(1). The main purpose of this paper is to investigate the distinguishability of the input-output mappings phi[center dot] : Kappa -> C-t[0, T], psi[center dot]: -> C-1 [0, T] via semigroup theory. In this paper, it is shown that if the null space of the semigroup T(t) consists of only zero function, then the input-output mappings phi[center dot] and psi[center dot] have the distinguishability property. It is also shown that the types of the boundary conditions and the region on which the problem is defined play an important role in the distinguishability property of these mappings. Moreover, under the light of measured output data (boundary observations) f(t) :=k(u(0, t))u(x)(0, t) or/and h(t) :=k(u(1, t),ux(l, t), the values k(00) and k(01) of the unknown diffusion coefficient k(u(x, t)) at (x, t) = (0, 0) and (x, t) = (1, 0), respectively, can be determined explicitly. In addition to these, the values k(u) (psi(0)) and k(u)(psi(1)) of the unknown coefficient k(u (x, t)) at (x, t) = (0, 0) and (x, t) = (1, 0), respectively, are also determined via the input data. Furthermore, it is shown that measured output data f(t) and h(t) can be determined analytically by an integral representation. Hence the input-output mappings phi[center dot]: Kappa -> C-1[0, T], psi[center dot]: Kappa -> C-1 [0, T] are given explicitly in terms of the semigroup. Copyright (D 2007 John Wiley & Sons, Ltd.