An inverse time-dependent source problem for the heat equation

Hazanee, A.; Ismailov, Mansur I.; Lesnic, D.; Керимов, Н. Б.

doi:10.1016/j.apnum.2013.02.004

Cited by 38 publications

(21 citation statements)

References 15 publications

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“…As it happened previously with some of our investigations [13,14], we report that the secondorder Tikhonov regularization has produced more accurate results than the zeroth-or first-order regularization and therefore, only the numerical results obtained using the former regularization are illustrated in this section. A popular method for choosing the regularization parameter is the generalised cross-validation (GCV) criterion, which is based on minimising the following GCV function, [32]:…”

Section: Examplementioning

confidence: 83%

“…Inverse time-dependent source problems for the heat equation with local, nonlocal, integral or nonclassical (boundary) conditions have become the point of interest in many recent papers, [10,12,13,14,17,31,33], to name only a few. In the present paper, we consider yet another reconstruction of a time-dependent heat source from an integral over-determination measurement of the thermal energy of the system and a new dynamic-type boundary condition.…”

Section: Introductionmentioning

confidence: 99%

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An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

Hazanee

Lesnic

Ismailov

et al. 2015

Applied Mathematical Modelling

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This paper investigates the inverse problem of determining the time-dependent heat source and the temperature for the heat equation with a non-classical boundary and an integral over-determination conditions. The existence, uniqueness and continuous dependence upon the data of the classical solution of the inverse problem is shown by using the generalised Fourier method. Furthermore in the numerical process, the boundary element method (BEM) together with the second-order Tikhonov regularization is employed with the choice of regularization parameter based on the generalised cross-validation (GCV) criterion. Numerical results are presented and discussed.

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Section: Examplementioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

Hazanee

Lesnic

Ismailov

et al. 2015

Applied Mathematical Modelling

Self Cite

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“…The inverse problem of determining source term in heat equation with the same boundary condition and integral overdetermination condition is investigated both theoretically and numerically in [21]. Determination of time-dependent source term in the heat equation with nonlocal boundary conditions is studied theoretically in [22] and numerically in [23].…”

Section: Introductionmentioning

confidence: 99%

An inverse diffusion problem with nonlocal boundary conditions

Ismailov¹,

Oğur²

2015

Numerical Methods Partial

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This article considers the inverse problem of identification of a time-dependent thermal diffusivity together with the temperature in an one-dimensional heat equation with nonlocal boundary and integral overdetermination conditions when a heat exchange takes place across boundary of the material. The well-posedness of the problem is studied under some regularity, and consistency conditions on the data of the problem together with the nonnegativity condition on the Fourier coefficients of the initial data and source term. The inverse problem is also studied numerically by using the Crank-Nicolson finite difference scheme combined with predictor-corrector technique. The numerical examples are presented and discussed.

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“…For a more comprehensive overview of literature dealing with integral overdetermination within the framework of IPs for parabolic, hyperbolic and Navier-Stokes equations, we refer the reader e.g. to [2][3][4][5][6][7][8] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A nonlinear parabolic integro-differential problem with an unknown Dirichlet boundary condition

Grimmonprez

Slodička

2015

Journal of Computational and Applied Mathematics

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a b s t r a c tA nonlinear parabolic integro-differential equation ∂ t g (u) with a known Neumann boundary condition on a part of the boundary and an unknown Dirichlet boundary condition α(t) on the other part of the boundary is studied. The inverse problem of identifying the unknown time-dependent function α(t) from an additional integral measurement E(t) =  Ω g (u(t, x)) dx is investigated. The well-posedness of the problem in suitable function spaces is shown and a numerical time-discrete scheme for approximations is designed. Convergence of the proposed scheme is supported by a numerical experiment.

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An inverse time-dependent source problem for the heat equation

Cited by 38 publications

References 15 publications

An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

An inverse diffusion problem with nonlocal boundary conditions

A nonlinear parabolic integro-differential problem with an unknown Dirichlet boundary condition

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