Wavelet and error estimation of surface heat flux. (English) Zbl 1019.65074
The authors discuss the determination of the heat flux \( u_x(x,t)\) for \( 0<x<1 \) from the following problem:
\[
\begin{cases} u_{xx} = u_t, \quad & x \geq 0, t>0 , \\ u(x,0) = 0, \quad ,& x \geq 0, \\ u(1,t) = g(x), \quad & t \geq 0, u|_{t \to \infty}\text{ bounded.}\end{cases}
\]
They present a wavelet regularization method for this ill-posed problem. An error estimate and the convergence of the regularizations approximate solution at zero are obtained.
Reviewer: Wanguo Zhang (Shanghai)
MSC:
| 65M30 | Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs |
| 35K05 | Heat equation |
| 35R25 | Ill-posed problems for PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35R30 | Inverse problems for PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
inverse heat conduction; heat flux; regularization; wavelet; ill-posed problem; error estimate; convergenceReferences:
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