Source term identification for an axisymmetric inverse heat conduction problem
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TLDR
A simplified Tikhonov regularization method is applied to formulate regularized solution, which is stably convergent to the exact one with a logarithmic type error estimate.Abstract:
We consider an inverse heat source problem of determining the heat source term from the final temperature history of a cylinder. This problem is ill-posed. A simplified Tikhonov regularization method is applied to formulate regularized solution, which is stably convergent to the exact one with a logarithmic type error estimate.read more
Citations
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Journal ArticleDOI
Lectures on Cauchy’s Problem in Linear Partial Differential Equations. By J. Hadamard. Pp. viii+316. 15s.net. 1923. (Per Oxford University Press.)
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Thermo-viscoelastic materials with fractional relaxation operators
TL;DR: In this article, a new model of linear thermo-viscoelasticity for isotropic media taking into consideration the rheological properties of the volume with fractional relaxation operators is given.
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Application of the method of fundamental solutions and radial basis functions for inverse transient heat source problem
TL;DR: The numerical results show that the proposed θ -method with the method of fundamental solution and radial basis functions is easy to implement and pretty accurate and the accuracy of the results does not depend on the value of the θ parameter.
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Solving the inverse problem of identifying an unknown source term in a parabolic equation
TL;DR: The weighted homotopy analysis method (WHAM) is used for solving the inverse problem of determining an unknown source term in a parabolic equation with the leading coefficient depending on time and space variables under a final overdetermination condition.
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Determination of space–time-dependent heat source in a parabolic inverse problem via the Ritz–Galerkin technique
TL;DR: In this article, three inverse problems of reconstructing the time-dependent, spacewise-dependent and both initial condition and heat source in the one-dimensional heat equation are considered.
References
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Handbook of Mathematical Functions
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Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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