Source term identification for an axisymmetric inverse heat conduction problem

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.

[1]  Chu-Li Fu,et al.  Two regularization methods for a spherically symmetric inverse heat conduction problem , 2008 .

[2]  J. Cannon Determination of an Unknown Heat Source from Overspecified Boundary Data , 1968 .

[3]  谭永基,et al.  A CONDITIONAL STABILITY FOR AN INVERSE PROBLEM ARISING IN GROUNDWATER POLLUTION , 2005 .

[4]  William Rundell,et al.  Identification of a discontinuous source in the heat equation , 2001 .

[5]  J. Hadamard,et al.  Lectures on Cauchy's Problem in Linear Partial Differential Equations , 1924 .

[6]  Mehdi Dehghan,et al.  Determination of a control parameter in a one-dimensional parabolic equation using the method of radial basis functions , 2006, Math. Comput. Model..

[7]  Wei Cheng,et al.  A modified Tikhonov regularization method for a spherically symmetric three-dimensional inverse heat conduction problem , 2007, Math. Comput. Simul..

[8]  Masahiro Yamamoto,et al.  Conditional stability in determining a heat source , 2004 .

[9]  William Rundell,et al.  Unicity in an Inverse Problem for an Unknown Reaction Term in a Reaction-Diffusion Equation , 1985 .

[10]  Vu Kim Tuan,et al.  An inverse problem for the heat equation , 2010 .

[11]  John R. Cannon,et al.  Uniqueness and stability of 3D heat sources , 1991 .

[12]  Ulrich Tautenhahn,et al.  Lavrentiev Regularization for Linear Ill-Posed Problems under General Source Conditions , 2004 .

[13]  Chu-Li Fu,et al.  Two regularization methods for an axisymmetric inverse heat conduction problem , 2009 .

[14]  Li Kaitai,et al.  An inverse parabolic problem for nonlinear source term with nonlinear boundary conditions , 2003 .

[15]  Li Kaitai,et al.  An inverse parabolic problem for nonlinear source term with nonlinear boundary conditions , 2003 .

[16]  A. Kirsch An Introduction to the Mathematical Theory of Inverse Problems , 1996, Applied Mathematical Sciences.

[17]  Dang Duc Trong,et al.  Nonhomogeneous heat equation: Identification and regularization for the inhomogeneous term , 2005 .

[18]  A. J. Silva Neto,et al.  Two‐dimensional inverse heat conduction problem of estimating the time‐varying strength of a line heat source , 1992 .

[19]  Chu-Li Fu,et al.  Simplified Tikhonov and Fourier regularization methods on a general sideways parabolic equation , 2004 .

[20]  D. A. Murio,et al.  Source term identification in 1-D IHCP , 2004 .

[21]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[22]  Afet Golayoglu Fatullayev Numerical solution of the inverse problem of determining an unknown source term in a heat equation , 2002, Math. Comput. Simul..

[23]  Diego A. Murio,et al.  Identification of source terms in 2-D IHCP , 2004 .

[24]  J. Cannon,et al.  Structural identification of an unknown source term in a heat equation , 1998 .

[25]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[26]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[27]  Bithin Datta,et al.  Optimal Identification of Ground-Water Pollution Sources and Parameter Estimation , 2001 .

[28]  R. Van Keer,et al.  Parameter identification by a single injection-extraction well , 2002 .

[29]  A. Carasso Determining Surface Temperatures from Interior Observations , 1982 .

[30]  Daniel Lesnic,et al.  The boundary-element method for the determination of a heat source dependent on one variable , 2006 .