The Experts below are selected from a list of 306 Experts worldwide ranked by ideXlab platform
Ali Demir - One of the best experts on this subject based on the ideXlab platform.
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Inverse Problem for Determination of An Unknown Coefficient in the Time Fractional Diffusion Equation
Communications in Mathematics and Applications, 2018Co-Authors: Ali Demir, Mine Aylin BayrakAbstract:The fundamental concern of this article is to apply the residual power series method (RPSM) effectively to determine of the Unknown Coefficient in the time fractional diffusion equation in the Caputo sense with over measured data. First, the fractional power series solution of inverse problem of Unknown Coefficient is obtained by residual power series method. Finally, efficiency and accuracy of the present method is illustrated by numerical examples.
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identification of the Unknown diffusion Coefficient in a linear parabolic equation via semigroup approach
Advances in Difference Equations, 2014Co-Authors: Ebru Ozbilge, Ali DemirAbstract:This article presents a semigroup approach to the mathematical analysis of the inverse parameter problems of identifying the Unknown parameters and q in the linear parabolic equation , with mixed boundary conditions , . The main purpose of this paper is to investigate the distinguishability of the input-output mapping , via semigroup theory. In this paper, it is shown that if the nullspace of the semigroup consists of only the zero function, then the input-output mapping 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 at and also the Unknown Coefficient q. Furthermore, it is shown that measured output data can be determined analytically by an integral representation. Hence the input-output mapping is given explicitly in terms of the semigroup.
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Identification of the Unknown Coefficient in a quasi-linear parabolic equation by a semigroup approach
Journal of Inequalities and Applications, 2013Co-Authors: Ebru Ozbilge, Ali DemirAbstract:This article presents a semigroup approach to the mathematical analysis of the inverse Coefficient problems of identifying the Unknown Coefficient a(x, t )i n the quasi-linear parabolic equation ut(x, t )= uxx(x, t )+ a(x, t)u(x, t) with Dirichlet boundary conditions u(0, t )= ψ0, u(1, t )= ψ1. It is shown that the Unknown Coefficient a(x, t )c an be approximately determined via the semigroup approach.
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semigroup approach for identification of the Unknown diffusion Coefficient in a linear parabolic equation with mixed output data
Boundary Value Problems, 2013Co-Authors: Ebru Ozbilge, Ali DemirAbstract: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 ut(x, t )=( k(x)ux(x, t))x with mixed boundary conditions k(0)ux(0, t )= ψ0, u(1, t )= ψ1. The aim of this paper is to investigate the distinguishability of the input-output mappings � [· ]: K → H 1,2 [0, T], � [· ]: K → H 1,2 [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 � [· ]a nd� [·] 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)ux(1, t), the values k(0) and k(1) of the Unknown diffusion Coefficient k(x )a tx =0a ndx = 1, respectively, can be determined explicitly. In addition to these, the values k � (0) and k � (1) of the Unknown Coefficient k(x )a tx =0a ndx =1 , respectively, are also determined via the input data. Furthermore, it is shown that measured output data f (t )a ndh(t) can be determined analytically by an integral representation. Hence the input-output mappings � [· ]: K → H 1,2 [0, T], � [· ]: K → H 1,2 [0, T] are given explicitly in terms of the semigroup.
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analysis for the identification of an Unknown diffusion Coefficient via semigroup approach
Mathematical Methods in The Applied Sciences, 2009Co-Authors: Ali Demir, Ebru OzbilgeAbstract:This paper presents a semigroup approach for the mathematical analysis of the inverse Coefficient problems of identifying the Unknown Coefficient k(ux) in the inhomogenenous quasi-linear parabolic equation ut(x, t)=(k(ux)ux(x, t))x +F(u), with the Dirichlet boundary conditions u(0, t)=ψ0, u(1, t)=ψ1 and source function F(u). The main purpose of this paper is to investigate the distinguishability of the input–output mappings Φ[·]:C1[0, T], Ψ[·]:C1[0, T] via semigroup theory. Copyright © 2009 John Wiley & Sons, Ltd.
Alemdar Hasanov - One of the best experts on this subject based on the ideXlab platform.
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Identification of an Unknown Coefficient in KdV equation from final time measurement
Journal of Inverse and Ill-posed Problems, 2016Co-Authors: K. Sakthivel, Alemdar Hasanov, S. Gnanavel, Raju K. GeorgeAbstract:AbstractIn this article, we study an inverse problem of reconstructing a space dependent Coefficient in a generalized Korteweg–de Vries (KdV) equation arising in physical systems with variable topography from final time overdetermination data. First the identification problem is transformed into an optimization problem by using optimal control framework and existence of a minimizer for the cost functional is established. Then we prove a stability estimate for retrieving the Unknown Coefficient in KdV equation with the upper bound of given measurements. The local uniqueness of the Coefficient is also discussed.
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Identification of Unknown diffusion Coefficient in pure diffusive linear model of chronoamperometry. I. The theory
Journal of Mathematical Chemistry, 2010Co-Authors: Alemdar HasanovAbstract:Coefficient identification problem for diffusion equation u _ t ( x , t ) = ( D ( x ) u _ x ( x , t ))_ x arising in chronoamperometry is studied. The adjoint problem approach is developed for the case when the output measured data is given in the form of left/right flux. Analytical formulas for determination of the values D (0), D ( L ) at the endpoints x = 0; L , of the Unknown Coefficient D ( x ), via the solution v ( x , t ) of the constant Coefficient equation v _ t ( x , t ) = D v _ xx ( x , t ) is obtained. The integral identity relating solutions of the forward and corresponding adjoint problems is derived. This integral identity permits one to prove the monotonicity and invertibility of input-output map, as well as formulate the gradient of the cost functional via the solutions of the direct and adjoint problems.
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identification of the Unknown diffusion Coefficient in a linear parabolic equation by the semigroup approach
Journal of Mathematical Analysis and Applications, 2008Co-Authors: Ali Demir, Alemdar HasanovAbstract:In this article, we study the semigroup approach for the mathematical analysis of the inverse Coefficient problems of identifying the Unknown Coefficient k(x) in the linear parabolic equation ut(x,t)=(k(x)ux(x,t))x, with Dirichlet boundary conditions u(0,t)=ψ0, u(1,t)=ψ1. Main goal of this study is to investigate the distinguishability of the input–output mappings Φ[⋅]:K→C1[0,T], Ψ[⋅]:K→C1[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 Φ[⋅] and Ψ[⋅] have the distinguishability property. Moreover, 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 by making use of measured output data (boundary observations) f(t):=k(0)ux(0,t) or/and h(t):=k(1)ux(1,t). 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 Φ[⋅]:K→C1[0,T], Ψ[⋅]:K→C1[0,T] are given explicitly in terms of the semigroup. Finally by using all these results, we construct the local representations of the Unknown Coefficient k(x) at the end points x=0 and x=1.
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Determination of Unknown Coefficient in a non-linear elliptic problem related to the elastoplastic torsion of a bar
IMA Journal of Applied Mathematics, 2007Co-Authors: Alemdar Hasanov, Arzu ErdemAbstract:The inverse problem of determining the Unknown Coefficient of the non-linear differential equation of torsional creep is studied. The Unknown Coefficient g = g (ξ 2 ) depends on the gradient ξ : = |r u | of the solution u ( x ) , x 2 Ω � R n , of the direct problem. It is proved that this gradient is bounded in C-norm. This permits one to choose the natural class of admissible Coefficients for the considered inverse problem. The continuity in the norm of the Sobolev space H 1 (Ω) of the solution u ( x ; g ) of the direct problem with respect to the Unknown Coefficient g = g (ξ 2 ) is obtained in the following sense: k u ( x ; g ) − u ( x ; g m )k 1 → 0 when g m (η) → g (η) point-wise as m → ∞ . Based on these results, the existence of a quasi-solution of the inverse problem in the considered class of admissible Coefficients is obtained. Numerical examples related to determination of the Unknown Coefficient are presented.
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error analysis of a multisingular inverse Coefficient problem for the sturm liouville operator based on boundary measurement
Applied Mathematics and Computation, 2004Co-Authors: Alemdar HasanovAbstract:In this paper we study the inverse problem of determining the Unknown leading Coefficient k=k(x) of the linear Sturm-Liouville operator Au=-(k(x)u^'(x))^'+q(x)u(x), x@?(0,1), from boundary measurements, when u^'(x) or/and u^'^'(x) vanishes at several, called singular, points of the interval (0,1). As a result the considered inverse problem has simultaneously different types (moderate or severely) of ill-conditioned situations in different parts of the interval (0,1). The presented inverse polynomial method permits use of a priori information about singular points either to increase the order of the polynomial approximation in each subinterval or to obtain an artificial Cauchy data for the Unknown Coefficient. Error estimations for the polynomial approximations are presented for well-conditioned, as well as for ill-conditioned situations. The behaviour of the inverse problem solution with respect to both types (Dirichlet and Neumann) of noisy data is analyzed. The obtained results are illustrated by various numerical examples.
Ebru Ozbilge - One of the best experts on this subject based on the ideXlab platform.
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identification of the Unknown diffusion Coefficient in a linear parabolic equation via semigroup approach
Advances in Difference Equations, 2014Co-Authors: Ebru Ozbilge, Ali DemirAbstract:This article presents a semigroup approach to the mathematical analysis of the inverse parameter problems of identifying the Unknown parameters and q in the linear parabolic equation , with mixed boundary conditions , . The main purpose of this paper is to investigate the distinguishability of the input-output mapping , via semigroup theory. In this paper, it is shown that if the nullspace of the semigroup consists of only the zero function, then the input-output mapping 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 at and also the Unknown Coefficient q. Furthermore, it is shown that measured output data can be determined analytically by an integral representation. Hence the input-output mapping is given explicitly in terms of the semigroup.
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Identification of the Unknown Coefficient in a quasi-linear parabolic equation by a semigroup approach
Journal of Inequalities and Applications, 2013Co-Authors: Ebru Ozbilge, Ali DemirAbstract:This article presents a semigroup approach to the mathematical analysis of the inverse Coefficient problems of identifying the Unknown Coefficient a(x, t )i n the quasi-linear parabolic equation ut(x, t )= uxx(x, t )+ a(x, t)u(x, t) with Dirichlet boundary conditions u(0, t )= ψ0, u(1, t )= ψ1. It is shown that the Unknown Coefficient a(x, t )c an be approximately determined via the semigroup approach.
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semigroup approach for identification of the Unknown diffusion Coefficient in a linear parabolic equation with mixed output data
Boundary Value Problems, 2013Co-Authors: Ebru Ozbilge, Ali DemirAbstract: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 ut(x, t )=( k(x)ux(x, t))x with mixed boundary conditions k(0)ux(0, t )= ψ0, u(1, t )= ψ1. The aim of this paper is to investigate the distinguishability of the input-output mappings � [· ]: K → H 1,2 [0, T], � [· ]: K → H 1,2 [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 � [· ]a nd� [·] 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)ux(1, t), the values k(0) and k(1) of the Unknown diffusion Coefficient k(x )a tx =0a ndx = 1, respectively, can be determined explicitly. In addition to these, the values k � (0) and k � (1) of the Unknown Coefficient k(x )a tx =0a ndx =1 , respectively, are also determined via the input data. Furthermore, it is shown that measured output data f (t )a ndh(t) can be determined analytically by an integral representation. Hence the input-output mappings � [· ]: K → H 1,2 [0, T], � [· ]: K → H 1,2 [0, T] are given explicitly in terms of the semigroup.
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analysis for the identification of an Unknown diffusion Coefficient via semigroup approach
Mathematical Methods in The Applied Sciences, 2009Co-Authors: Ali Demir, Ebru OzbilgeAbstract:This paper presents a semigroup approach for the mathematical analysis of the inverse Coefficient problems of identifying the Unknown Coefficient k(ux) in the inhomogenenous quasi-linear parabolic equation ut(x, t)=(k(ux)ux(x, t))x +F(u), with the Dirichlet boundary conditions u(0, t)=ψ0, u(1, t)=ψ1 and source function F(u). The main purpose of this paper is to investigate the distinguishability of the input–output mappings Φ[·]:C1[0, T], Ψ[·]:C1[0, T] via semigroup theory. Copyright © 2009 John Wiley & Sons, Ltd.
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Identification of an Unknown Coefficient Approximately
AIP Conference Proceedings, 2009Co-Authors: Ebru Ozbilge, Ali DemirAbstract: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) = Ψ0, u(1,t) = Ψ1. It is shown that the Unknown Coefficient a(x, t) can be approximately determined via semigroup approach.
Mine Aylin Bayrak - One of the best experts on this subject based on the ideXlab platform.
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Inverse Problem for Determination of An Unknown Coefficient in the Time Fractional Diffusion Equation
Communications in Mathematics and Applications, 2018Co-Authors: Ali Demir, Mine Aylin BayrakAbstract:The fundamental concern of this article is to apply the residual power series method (RPSM) effectively to determine of the Unknown Coefficient in the time fractional diffusion equation in the Caputo sense with over measured data. First, the fractional power series solution of inverse problem of Unknown Coefficient is obtained by residual power series method. Finally, efficiency and accuracy of the present method is illustrated by numerical examples.
Tang Qingguo - One of the best experts on this subject based on the ideXlab platform.
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B-spline estimation for semiparametric varying-Coefficient partially linear regression with spatial data
Journal of Nonparametric Statistics, 2013Co-Authors: Tang QingguoAbstract:This paper considers a varying-Coefficient partially linear regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the Unknown parameters and Coefficient functions. Under mild regularity assumptions, the asymptotic distribution of the estimator of the Unknown parameter vector is established. The global convergence rates of the B-spline estimators of the Unknown Coefficient functions are established. The asymptotic distributions of the B-spline estimators of the Unknown Coefficient functions are also derived. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Boston housing data is used to illustrate our proposed methodology.
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Asymptotic Normality of M-Estimators for Varying Coefficient Models with Longitudinal Data
Communications in Statistics - Theory and Methods, 2009Co-Authors: Tang Qingguo, Cheng LongshengAbstract:This article considers a nonparametric varying Coefficient regression model with longitudinal observations. The relationship between the dependent variable and the covariates is assumed to be linear at a specific time point, but the Coefficients are allowed to change over time. A general formulation is used to treat mean regression, median regression, quantile regression, and robust mean regression in one setting. The local M-estimators of the Unknown Coefficient functions are obtained by local linear method. The asymptotic distributions of M-estimators of Unknown Coefficient functions at both interior and boundary points are established. Various applications of the main results, including estimating conditional quantile Coefficient functions and robustifying the mean regression Coefficient functions are derived. Finite sample properties of our procedures are studied through Monte Carlo simulations.
