Mean value methods for solving the heat equation backwards in time
arXiv:2011.14685
Abstract
We investigate an iterative mean value method for the inverse (and highly ill-posed) problem of solving the heat equation backwards in time. Semi-group theory is used to rewrite the solution of the inverse problem as the solution of a fixed point equation for an affine operator, with linear part satisfying special functional analytical properties. We give a convergence proof for the method and obtain convergence rates for the residual. Convergence rates for the iterates are also obtained under the so called source conditions.
13 pages. arXiv admin note: text overlap with arXiv:2011.08629