Regularization of the semilinear sideways heat equation

[1]  B. Blackwell,et al.  Inverse Heat Conduction: Ill-Posed Problems , 1985 .

[2]  Michael V. Klibanov,et al.  Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function , 2016 .

[3]  HIROSHI AKIMA,et al.  Algorithm 760: Rectangular-grid-data surface fitting that has the accuracy of a bicubic polynomial , 1996, TOMS.

[4]  Daniel Lesnic,et al.  On the Cauchy problem for semilinear elliptic equations , 2015 .

[5]  F. Berntsson Sequential Solution of the Sideways Heat Equation by Windowing of the Data , 2003 .

[6]  Fredrik Berntsson,et al.  Wavelet and Fourier Methods for Solving the Sideways Heat Equation , 1999, SIAM J. Sci. Comput..

[7]  C. Fu,et al.  A modified method for determining the surface heat flux of IHCP , 2007 .

[8]  G. Smith,et al.  Numerical Solution of Partial Differential Equations: Finite Difference Methods , 1978 .

[9]  B. Tomas Johansson,et al.  A boundary element method for a multi-dimensional inverse heat conduction problem , 2012, Int. J. Comput. Math..

[10]  Derek B. Ingham,et al.  Application of the boundary element method to inverse heat conduction problems , 1996 .

[11]  Jan S. Hesthaven,et al.  Spectral Methods for Time-Dependent Problems: Contents , 2007 .

[12]  Ji-Chuan Liu,et al.  A quasi-reversibility regularization method for an inverse heat conduction problem without initial data , 2013, Appl. Math. Comput..

[13]  U. Tautenhahn,et al.  Optimal stable approximations for the sideways heat equation , 1997 .

[14]  O. Burggraf An Exact Solution of the Inverse Problem in Heat Conduction Theory and Applications , 1964 .

[15]  Xiang-Tuan Xiong,et al.  Central difference method of a non-standard inverse heat conduction problem for determining surface heat flux from interior observations , 2006, Appl. Math. Comput..

[16]  M. M. Lavrentʹev,et al.  Ill-Posed Problems of Mathematical Physics and Analysis , 1986 .

[17]  Lars Eldén,et al.  Approximations for a Cauchy problem for the heat equation , 1987 .

[18]  Xiang-Tuan Xiong,et al.  Fourier regularization method of a sideways heat equation for determining surface heat flux , 2006 .

[19]  William L. Briggs,et al.  The DFT : An Owner's Manual for the Discrete Fourier Transform , 1987 .

[20]  Chein-Shan Liu An LGDAE Method to Solve Nonlinear Cauchy ProblemWithout Initial Temperature , 2014 .

[21]  F. Ginsberg On the Cauchy Problem for the One-Dimensional Heat Equation , 1963 .

[22]  Dinh Nho Hào,et al.  Methods for inverse heat conduction problems , 1998 .

[23]  Thomas I. Seidman,et al.  An 'optimal filtering' method for the sideways heat equation , 1990 .

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

[25]  Lars Eldén,et al.  The Numerical Solution of a Non-Characteristic Cauchy Probelm for a Parabolic Equation , 1983 .

[26]  Lars Eldén,et al.  Solving the sideways heat equation by a wavelet - Galerkin method , 1997 .