Identifying the coefficient of first-order in parabolic equation from final measurement data

Deng, Zui‐Cha; Jiang, Yu; Yang, Liu

doi:10.1016/j.matcom.2008.01.002

Cited by 34 publications

(14 citation statements)

References 26 publications

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“…In this work, we use the optimal control framework (see [7][8][9][10]21]) to discuss problem P. In the previous works, it has been shown that the optimization technique is an effective tool to deal with inverse heat conduction problems. However, due to the non-convexity of the cost functional, one cannot obtain the uniqueness of the minimizer or can obtain the local uniqueness at most (see, for instance [9,10,21]), which may diminish the utility value of the obtained results.…”

Section: Introductionmentioning

confidence: 99%

“…However, due to the non-convexity of the cost functional, one cannot obtain the uniqueness of the minimizer or can obtain the local uniqueness at most (see, for instance [9,10,21]), which may diminish the utility value of the obtained results. The new ingredient in this paper is that the global uniqueness and stability of the minimizer for the cost functional are proved.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimization method for the inverse problem of reconstructing the source term in a parabolic equation

Yang

Deng

Jiang

et al. 2009

Mathematics and Computers in Simulation

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimization method for the inverse problem of reconstructing the source term in a parabolic equation

Yang

Deng

Jiang

et al. 2009

Mathematics and Computers in Simulation

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“…For instance, an upper-base final temperature condition was chosen in [4] to identify a space-dependent heat source, and a similar version can be found in [2] where a Cauchy problem for a second-order parabolic equation was formulated for determining a space-dependent coefficient of a low-order derivative. Cauchy data have also been used in [5] for reconstructing numerically a temperature-dependent thermal conductivity or a heat source.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous determination of time and space-dependent coefficients in a parabolic equation

Hussein

Lesnic

2016

Communications in Nonlinear Science and Numerical Simulation

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This paper investigates a couple of inverse problems of simultaneously determining time and space dependent coefficients in the parabolic heat equation using initial and boundary conditions of the direct problem and overdetermination conditions. The measurement data represented by these overdetermination conditions ensure that these inverse problems have unique solutions. However, the problems are still ill-posed since small errors in the input data cause large errors in the output solution. To overcome this instability we employ the Tikhonov regularization method. The finite-difference method (FDM) is employed as a direct solver which is fed iteratively in a nonlinear minimization routine. Both exact and noisy data are inverted. Numerical results for a few benchmark test examples are presented, discussed and assessed with respect to the FDM mesh size discretisation, the level of noise with which the input data is contaminated, and the chosen regularization parameters.

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“…But an inevitable reality is that the inverse problem of identifying the coefficients in parabolic equations is often ill-posed, which leads to many difficulties on the study of the original inverse problem. For a helpful conversion from the original inverse problem to a tractable one, optimal control methods have been accepted by increasing researchers recently (for a survey of the studies see, for example [7][8][9][10][11][12]). Here, we mostly recall the studies of inverse problems on reaction-diffusion equations to state our main motivation in the study from the aspect of theory research.…”

Section: Introductionmentioning

confidence: 99%

Solving the inverse problem of an SIS epidemic reaction–diffusion model by optimal control methods

Xiang

Liu

2015

Computers & Mathematics with Applications

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a b s t r a c tIn this contribution, a novel inverse problem on an SIS epidemic reaction-diffusion model is investigated by employing the optimal control methods. By setting a proper regular cost functional and choosing the coefficients to be identified as control variables, we embed the original inverse problem which is very difficult to solve into an optimal control problem. The existence of the optimal controls and the first order necessary optimality condition satisfied by the optimal controls are established, respectively. In particular, the local uniqueness and stability of the identification of the coefficients are proved by using analytical techniques.

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Identifying the coefficient of first-order in parabolic equation from final measurement data

Cited by 34 publications

References 26 publications

Optimization method for the inverse problem of reconstructing the source term in a parabolic equation

Optimization method for the inverse problem of reconstructing the source term in a parabolic equation

Simultaneous determination of time and space-dependent coefficients in a parabolic equation

Solving the inverse problem of an SIS epidemic reaction–diffusion model by optimal control methods

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