Point source localisation is generally modelled as a Lasso-type problem on measures. However, optimisation methods in non-Hilbert spaces, such the space of Radon measures, are much less developed than Hilbert spaces. Most numerical algorithms for point based Frank-Wolfe conditional gradient method, which ad hoc convergence theory developed. We develop extensions proximal-type to spaces This inc...

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase nverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is ore realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear ombination of...

In this paper we prove that the multidimensional Hele-Shaw problem with kinetic condition at the free boundary is the limit case of the Stefan problem with kinetic condition at the free boundary in the classical sense when the specific heat e goes to zero. The method is the use of a fixed point theorem; the key step is to construct a suitable function space in which we can get the existence and...