On the basis of the duality principle, we obtain sufficient conditions for the uniqueness of the solution in Holder classes for the considered inverse Stefan problems. We present examples in which the uniqueness property is lost when extending the set of admissible solutions....
one-dimensional one-phase inverse Stefan problemtwo-phase change caseWe extend the meshless method of fundamental solutions proposed in [B.T. Johansson, D. Lesnic, and T. Reeve, A method of fundamental solutions for the one-dimensional inverse Stefan problem, Appl. Math. Model. 35 (2011), ...
and related pre- cipitation problems, as well as to the inverse Stefan problem where either the This approach is readily applicable to multi-phase problems; moreover, the technique wasqualitatively Linear Ordinary Differential Equations and the One-Phase Stefan Problem 257 boundary...
Slota, D., The Application of the Homotopy Perturbation Method to One-Phase Inverse Stefan Problem, Int. Comm. Heat & Mass Transf., 37 (2010), 6, pp. 587-592D. Slota, Homotopy perturbation method for solving the two-phase inverse Stefan problem, Numer. Heat Tr. A-Appl., 59 (2011...
We investigate the identification problem for the one-phase Stefan problem. As the inverse Stefan problem is not well posed, an optimal control problem is considered instead. In the paper we develop a dual dynamic programming approach to derive sufficient approximate optimality conditions ...
We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a logarithmic stability estimate that shows that the inversion is ...
One-phase inverse stefan problem with an unknown distributed convection coefficientGol'dman, N. L.DOKLADY MATHEMATICS C/C OF DOKLADY- AKADEMIIA NAUK
Hetmaniok E., Słota D., Wituła R., Zielonka A.: Solution of the one-phase inverse Stefan problem by using the homotopy analysis method. Appl. Math. Modelling (in review).Edyta Hetmaniok, Damian Słota, Roman Wituła, Adam Zielonka, Solution of the one-phase inverse Stefan ...
one‐phase linear inverse Stefan problemThe efficient numerical solution of the one‐phase linear inverse Stefan and Cauchy–Stefan problems is a delicate task owing to the problems' susceptibility to the perturbation of the given data. In this context, heuristic a posteriori error indicators are ...
L. Lorenzi, "An identification problem for a one-phase Stefan problem," J. Inv. Ill-Posed Probl., 9, No. 6, 1-27 (2001).Lorenzi, L (2001) An identification problem for a one-phase Stefan problem. J. Inverse Ill-Posed Probl. 9: pp. 1-...