Fourier regularization of an one-dimensional non-standard inverse heat conduction problem. (Chinese. English summary) Zbl 1007.35098
Summary: The following non-standard inverse heat conduction problem arises in various applications
\[
\begin{cases} u_t+u_x= u_{xx}, & 0\leq x<\infty,\;0<t <\infty,\\ u(1,t)=g(t), & 0\leq t<\infty,\\ u(x,0)=0, & x\geq 0.\end{cases}
\]
This problem is seriously ill-posed. In this paper, this problem is regularized by a Fourier method and an error estimate is given.
MSC:
| 35R25 | Ill-posed problems for PDEs |
| 35R30 | Inverse problems for PDEs |
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
