Existence and construction of solutions of dissipative inverse problems
Publikation/Tidskrift/Serie: Journal of Mathematical Analysis and Applications
The problem considered here is that of simultaneously reconstructing spatially dependent velocity and dissipation profiles for a one-dimensional medium using a finite time trace of normal incidence reflection data measured on one side of the medium. It is shown that if the sup norm of the reflection data is bounded in a particular way, then this inverse problem is guaranteed to have a solution. A numerical algorithm which is based on this existence proof is used to illustrate the reconstruction process.
- Mathematics and Statistics
- ISSN: 0022-247X