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RISS 인기검색어
- 검색키워드
- 저자 : Deiveegan, A. (검색결과 2 건)
- 무료
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- 유료
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Generalized Tikhonov methods for an inverse source problem of the time-fractional diffusion equation
Ma, Yong-Ki,Prakash, P.,Deiveegan, A. Elsevier 2018 Chaos, solitons, and fractals Vol.108 No.-
<P><B>Abstract</B></P> <P>In this paper, we identify the unknown space-dependent source term in a time-fractional diffusion equation with variable coefficients in a bounded domain where additional data are consider at a fixed time. Using the generalized and revised generalized Tikhonov regularization methods, we construct regularized solutions. Convergence estimates for both methods under an <I>a-priori</I> and <I>a-posteriori</I> regularization parameter choice rules are given, respectively. Numerical example shows that the proposed methods are effective and stable.</P> <P><B>Highlights</B></P> <P> <UL> <LI> This paper investigates the problem of determining a space-dependent source term in a time-fractional diffusion equation with variable coefficients in a bounded domain where additional data are consider at a fixed time. Using the generalized and revised generalized Tikhonov regularization methods, we construct regularized solutions. </LI> <LI> One important feature of our paper is that the Convergence estimates for both methods under a-priori and a-posteriori regularization parameter choice rules are given, respectively. </LI> <LI> In this work we have extended the revised generalized Tikhonov regularization method for the inverse problem of determining the source term in time-fractional diffusion equation. The obtained result shows a new contribution in the field of fractional diffusion equation. </LI> <LI> However it should be emphasized that the revised generalized Tikhonov regularization method is mainly concerned with inverse source problems for the heat equation and there have been no attempts made for studying the time-fractional diffusion problem. </LI> </UL> </P>
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Optimization method for determining the source term in fractional diffusion equation
Ma, Yong-Ki,Prakash, P.,Deiveegan, A. Elsevier 2019 Mathematics and computers in simulation Vol.155 No.-
<P><B>Abstract</B></P> <P>In this paper, we determine a spacewise dependent source in one-dimensional fractional diffusion equation. On the basis of the optimal control method, the existence, uniqueness and stability of the minimizer for the cost functional are established. The Landweber iteration method is applied to the inverse problem.</P> <P><B>Highlights</B></P> <P> <UL> <LI> In this paper the inverse problem is transformed into an optimization problem. </LI> <LI> The uniqueness and stability of minimizer are deduced from the necessary condition. </LI> <LI> We have extended the method for inverse problem of fractional diffusion equation. </LI> <LI> There have been few attempts made for studying fractional problems by optimization. </LI> </UL> </P>
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