Ten lectures on wavelets
Sideways heat equation and wavelets
Modelling 94 Proceedings of the 1994 international symposium on Mathematical modelling and computational methods
Wavelet and Fourier Methods for Solving the Sideways Heat Equation
SIAM Journal on Scientific Computing
Simplified Tikhonov and Fourier regularization methods on a general sideways parabolic equation
Journal of Computational and Applied Mathematics
Determining surface temperature and heat flux by a wavelet dual least squares method
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
Two regularization methods and the order optimal error estimates for a sideways parabolic equation
Computers & Mathematics with Applications
Fourier regularization method for solving the surface heat flux from interior observations
Mathematical and Computer Modelling: An International Journal
Regional gradient observability for distributed semilinear parabolic systems
Journal of Dynamical and Control Systems
Regularization methods for unknown source in space fractional diffusion equation
Mathematics and Computers in Simulation
| Hi-index | 7.31 |
We consider the determination of the surface heat flux of a body from a measured temperature history at a fixed location inside the body. Mathematically, it is formulated as a problem for the one-dimensional heat equation in a quarter plane with data given along the line x = 1, and the gradient of the solution is wanted for 0 x 1. This problem is severely ill-posed and there are few theoretic results. The results available in the literatures are mainly devoted to the case of determining surface temperature. The aim of this paper is to indicate a possibility of a new approach for solving this problem based on an application of wavelet basis decomposition of measured data. The error estimate with Hölder type is given and the convergence of regularization approximation solution at zero is also obtained which is a difficult problem left over by some authors.