Calculation of the surface temperature and heat flux on one side of a wall from measurements on the opposite side

Manselli, Paolo; Miller, Keith

doi:10.1007/bf01796543

Cited by 65 publications

(20 citation statements)

References 7 publications

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“…Stability estimates have been obtained, by methods quite different from ours and in a different functional setting, by Cannon [2], [3], [4], [5]. Similar problems have been discussed by Anderssen and Saull [1], Glasko, Zaharov and Kolp [6] and P. Manselli and K. Miller [7].…”

Section: Introductionmentioning

confidence: 68%

A note on an ill-posed problem for the heat equation

Talenti¹,

Vessella²

1982

J Aust Math Soc A

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In this paper an ill-posed problem for the heat equation is investigated. Solutions u to the equation u, -u xx = 0, which are approximately known on the positive half-axis t = 0 and on some vertical lines x -xj,... ,x = x n , are considered and stability estimates of these solutions are presented. We assume an a priori bound, governing the heat flow across the boundary x = 0. 1980 Mathematics subject classification (Amer. Math. Soc): 35 K 05.

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Section: Introductionmentioning

confidence: 68%

A note on an ill-posed problem for the heat equation

Talenti¹,

Vessella²

1982

J Aust Math Soc A

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“…The convolution method aims at mollifying the equation but the mollification method aims at mollifying the improper data [30,14]. For example, Manselli, Miller [26] and Murio [31,32] have used mollification methods to solve some ill-posed problems for the heat equation, but their method is working only on the Weierstrass kernel. In [14], Hào gave a choice of the mollification parameter and obtained a convergence estimate for a non-characteristic Cauchy problem of parabolic equations.…”

Section: Introductionmentioning

confidence: 99%

Convolution regularization method for backward problems of linear parabolic equations

Shi

Wang

Wei

2016

Applied Numerical Mathematics

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“…The main procedure of the mollification method is using the kernel function to construct a mollification operator by convolution with the measurement data. Manselli, Miller [14], and Murio [15,16] constructed mollification operators by using the Weierstrass kernel to solve some inverse heat conduction problems (IHCP). There have been reports on using the Gaussian kernel to solve the Cauchy problem of elliptic equations [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

A Numerical Approximation Method for the Inverse Problem of the Three-Dimensional Laplace Equation

Feng

2019

Mathematics

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In this article, an inverse problem with regards to the Laplace equation with non-homogeneous Neumann boundary conditions in a three-dimensional case is investigated. To deal with this problem, a regularization method (mollification method) with the bivariate de la Vallée Poussin kernel is proposed. Stable estimates are obtained under a priori bound assumptions and an appropriate choice of the regularization parameter. The error estimates indicate that the solution of the approximation continuously depends on the noisy data. Two experiments are presented, in order to validate the proposed method in terms of accuracy, convergence, stability, and efficiency.

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Calculation of the surface temperature and heat flux on one side of a wall from measurements on the opposite side

Cited by 65 publications

References 7 publications

A note on an ill-posed problem for the heat equation

A note on an ill-posed problem for the heat equation

Convolution regularization method for backward problems of linear parabolic equations

A Numerical Approximation Method for the Inverse Problem of the Three-Dimensional Laplace Equation

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