Abstract
We consider the problem of reconstruction of the temperature from knowledge of the temperature and heat flux on a part of the boundary of a bounded planar domain containing corner points. An iterative method is proposed involving the solution of mixed boundary value problems for the heat equation (with time-dependent conductivity). These mixed problems are shown to be well-posed in a weighted Sobolev space.
| Original language | English |
|---|---|
| Pages (from-to) | 122-131 |
| Number of pages | 10 |
| Journal | International Journal of Computing Science and Mathematics |
| Volume | 3 |
| Issue number | 1/2 |
| DOIs | |
| Publication status | Published - 2010 |
Keywords
- Cauchy problem
- corner domains
- heat equations
- ill-posed
- iterative regularisation
- weighted Sobolev space
- temperature reconstruction
- heat flux
- mixed boundary value
- time-dependent conductivity