Özbilge Kahveci, Ebru

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Profile URL
https://hdl.handle.net/20.500.14365/7233
Name Variants
Ozbilge, E.
Ozbilgekahveci, Ebru
Ozbilge, Ebru
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Email Address
ebru.ozbilge@ieu.edu.tr
Main Affiliation
02.02. Mathematics
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Former Staff
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ORCID ID
0000-0002-2998-8134
Scopus Author ID
15081438700
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61158A36C0A8A162
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WoS Researcher ID
GAV-1155-2022

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60

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545

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24

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20

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WoS Citation Count

128

Scopus Citation Count

144

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9

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8

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WoS Citations per Publication

5.33

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6.00

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9

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JournalCount
Boundary Value Problems4
Mathematıcal Methods in the Applıed Scıences3
AIP Conference Proceedings3
Applıed Mathematıcs And Computatıon2
Journal of Inequalıtıes And Applıcatıons2
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Now showing 1 - 10 of 24
  • Thumbnail Image
    Article
    Citation - WoS: 1
    Citation - Scopus: 2
    Convergence Theorem for a Numerical Method of a 1d Coefficient Inverse Problem
    (Taylor & Francis Ltd, 2014) Özbilge Kahveci, Ebru
    An approximately globally convergent numerical method proposed by Beilina and Klibanov for a coefficient inverse problem related to the hyperbolic equation c(x)u(tt) = u(xx) is studied. While the global convergence of this method has been proved for the 3D case, in 1D case, it was proved only partially. The last case is of an interest, since it was demonstrated that the 1D version of this method works well for a set of experimental data. In this paper, a complete proof of convergence of this method in 1D is presented.
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    Article
    Solvability Conditions and Monotone Iterative Scheme for Boundary-Value Problems Related To Nonlinear Monotone Potential Operators
    (Taylor & Francis Ltd, 2010) Özbilge Kahveci, Ebru
    This article deals with boundary-value problems (BVPs) for the second-order nonlinear differential equations with monotone potential operators of type Au:= -del(k(vertical bar del u vertical bar(2))del u(x)) + q(u(2))u(x), x is an element of Omega subset of R(n). An analysis of nonlinear problems shows that the potential of the operator A as well as the potential of related BVP plays an important role not only for solvability of these problems and linearization of the nonlinear operator, but also for the strong convergence of solutions of corresponding linearized problems. A monotone iterative scheme for the considered BVP is proposed.
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    Article
    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.
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    Article
    An Analysis of Conservative Finite Difference Schemes for Differential Equations With Discontinuous Coefficients
    (Elsevier Science Inc, 2007) Özbilge Kahveci, Ebru
    A class of monotone conservative schemes is derived for the boundary value problem related to the Sturm-Liouville operator Au : = -(k(x)u'(x))' + q(x)u(x), with discontinuous coefficient k = k(x). The discrete analogous of the law of conservation are compared for the finite element and finite difference approaches. In the class of discontinuous coefficients, the necessary condition for conservativeness of the finite difference scheme is derived. The obtained one parametric family of conservative schemes permits one to construct new conservative schemes. The examples, presented for different discontinuous coefficients, and results show how the conservativeness conditions need to be taken into account in numerical solving boundary value problems. (c) 2007 Elsevier Inc. All rights reserved.
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    Conference Object
    An Application of Semigroup Method in a Parabolic Equation With Mixed Boundary Conditions
    (2008) Ozbilge E.
    This article presents analysis of the inverse coefficient problems of identifying the unknown diffusion coefficient in a quasi-linear parabolic equation, with mixed boundary conditions. By using semigroup theory we examined the distinguishability of the input-output mappings. If the null space of the semigroups consist of zero function, then we concluded that the input-output mappings have the distinguishability property. The values of k(u(0,0)) and k(u(1,t)) can be determined by making use of measured output data. Hence we redefine the new set of admissible coefficients. The semigroup representations of the input-output mappings are obtained in integral form. Moreover the input-output mappings are obtained explicitly in integral form. © 2008 American Institute of Physics.
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    Article
    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.
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    Article
    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.
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    Article
    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.
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    Article
    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.
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    Article
    Citation - WoS: 7
    Citation - Scopus: 8
    Determination of the Unknown Boundary Condition of the Inverse Parabolic Problems Via Semigroup Method
    (Springer International Publishing Ag, 2013) Özbilge Kahveci, Ebru
    In this article, a semigroup approach is presented for the mathematical analysis of inverse problems of identifying the unknown boundary condition u(1, t) = f (t) in the quasi-linear parabolic equation u(t)(x, t) = (k(u(x, t)) ux(x, t)) x, with Dirichlet boundary conditions u(0, t) = psi(0), u(1, t) = f (t), by making use of the over measured data u(x(0), t) = psi(1) and ux(x(0), t) = psi(2) separately. The purpose of this study is to identify the unknown boundary condition u(1, t) at x = 1 by using the over measured data u(x(0), t) = psi(1) and ux(x(0), t) = psi(2). First, by using over measured data as a boundary condition, we define the problem on Omega(T0) = {(x, t) is an element of R-2 : 0 < x < x(0), 0 < t <= T}, then the integral representation of this problem via a semigroup of linear operators is obtained. Finally, extending the solution uniquely to the closed interval [0, 1], we reach the result. The main point here is the unique extensions of the solutions on [0, x0] to the closed interval [0, 1] which are implied by the uniqueness of the solutions. This point leads to the integral representation of the unknown boundary condition u(1, t) at x = 1.