An inverse coefficient problem for the heat equation in the case of nonlocal boundary conditions

Керимов, Н. Б.; Ismailov, Mansur I.

doi:10.1016/j.jmaa.2012.06.046

Cited by 47 publications

(25 citation statements)

References 20 publications

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“…where ζ 1 and ζ 2 are the only two positive solutions to equation (22). Applying the increasing function g 4 side by side to both inequalities and taking into account that ξ satisfies equation (E4), it follows that (28) is equivalent to (R6).…”

Section: Explicit Formulae For the Unknown Thermal Coefficientsmentioning

confidence: 99%

Simultaneous Determination of Two Unknown Thermal Coefficients Through a Mushy Zone Model With an Overspecified Convective Boundary Condition

Ceretani¹,

Tarzia²

2016

JPHMT

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The simultaneous determination of two unknown thermal coefficients for a semi-infinite material under a phase-change process with a mushy zone according to the SolomonWilson-Alexiades model is considered. The material is assumed to be initially liquid at its melting temperature and it is considered that the solidification process begins due to a heat flux imposed at the fixed face. The associated free boundary value problem is overspecified with a convective boundary condition with the aim of the simultaneous determination of the temperature of the solid region, one of the two free boundaries of the mushy zone and two thermal coefficients among the latent heat by unit mass, the thermal conductivity, the mass density, the specific heat and the two coefficients that characterize the mushy zone. The another free boundary of the mushy zone, the bulk temperature and the heat flux and heat transfer coefficients at the fixed face are assumed to be known. According to the choice of the unknown thermal coefficients, fifteen phasechange problems arise. The study of all of them is presented and explicit formulae for * aceretani@austral.edu.ar † dtarzia@austral.edu.ar 1 the unknowns are given, beside necessary and sufficient conditions on data in order to obtain them. Formulae for the unknown thermal coefficients, with their corresponding restrictions on data, are summarized in a table.

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Section: Explicit Formulae For the Unknown Thermal Coefficientsmentioning

confidence: 99%

Simultaneous Determination of Two Unknown Thermal Coefficients Through a Mushy Zone Model With an Overspecified Convective Boundary Condition

Ceretani¹,

Tarzia²

2016

JPHMT

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“…The main difficulty for applying Fourier method is its basisness, i.e., expansion in terms of eigenfunctions of the auxiliary spectral problem [19] X (x) + λX(x) = 0, 0 ≤ x ≤ 1,…”

Section: A Auxiliary Spectral Problemmentioning

confidence: 99%

“…Since the function a(t) is space independent and boundary conditions are linear and homogeneous, the method of separation of variables is suitable for studying the inverse problem (1.1)-(1.4). The main difficulty for applying Fourier method is its basisness, i.e., expansion in terms of eigenfunctions of the auxiliary spectral problem [19] X (x) + λX(x) = 0, 0 ≤ x ≤ 1,…”

Section: A Auxiliary Spectral Problemmentioning

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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“…The inverse problem of finding the coefficient p(t) in the equation (1.1) with the nonlocal boundary conditions are considered in the papers [13][14][15][16]. In contrast to these papers, in present paper the boundary conditions are localized to the points x = 0 and x = 1.…”

Section: Introductionmentioning

confidence: 99%

Direct and inverse problems for the heat equation with a dynamic-type boundary condition

Керимов¹,

Ismailov

2015

IMA J Appl Math

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This paper considers the initial-boundary value problem for the heat equation with a dynamic type boundary condition. Under some regularity, consistency and orthogonality conditions, the existence, uniqueness and continuous dependence upon the data of the classical solution are shown by using the generalized Fourier method. This paper also investigates the inverse problem of finding a time-dependent coefficient of the heat equation from the data of integral overdetermination condition.

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An inverse coefficient problem for the heat equation in the case of nonlocal boundary conditions

Cited by 47 publications

References 20 publications

Simultaneous Determination of Two Unknown Thermal Coefficients Through a Mushy Zone Model With an Overspecified Convective Boundary Condition

Simultaneous Determination of Two Unknown Thermal Coefficients Through a Mushy Zone Model With an Overspecified Convective Boundary Condition

An inverse diffusion problem with nonlocal boundary conditions

Direct and inverse problems for the heat equation with a dynamic-type boundary condition

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