Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function
Abstract
We solve numerically the side Cauchy problem for a 1-D parabolic equation. The initial condition is unknown. This is an ill-posed problem. The main difference with previous results is that our equation is quasilinear, whereas known publications on this topic work only with linear PDEs. The key idea is to minimize a weighted Tikhonov functional with the Carleman Weight Function (CWF) in it. Roughly, given a reasonable bounded set of any size in a reasonable Hilbert space, one can choose the parameter of the CWF in such a way that this functional becomes strictly convex on that set.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 16, 2016
- Source ID
- 10.1515/jiip-2016-0039
Entities
People
- Anatoly G. Yagola
- Jingzhi Li
- Michael Klibanov
- Nikolaj A. Koshev
Organizations
- Army Research Office
- Moscow State University
- Office of Naval Research
- Russian Center for Science Information
- Southern University of Science and Technology
- United States Army Research Laboratory
- University of North Carolina at Charlotte