An approach for solving of a moving boundary problem

Authors:
Hadi Basirzadeh;Ali Vahidian Kamyad
Affiliations:
Department of Mathematics, Shahid Chamran University of Ahvaz, P.O. Box 61357-83151, Ahvaz, Iran;Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran
Venue:
Journal of Applied Mathematics and Computing
Year:
1986

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Abstract

In this paper we shall study moving boundary problems, and we introduce an approach for solving a wide range of them by using calculus of variations and optimization. First, we transform the problem equivalently into an optimal control problem by defining an objective function and artificial control functions. By using measure theory, the new problem is modified into one consisting of the minimization of a linear functional over a set of Radon measures; then we obtain an optimal measure which is then approximated by a finite combination of atomic measures and the problem converted to an infinite-dimensional linear programming. We approximate the infinite linear programming to a finite-dimensional linear programming. Then by using the solution of the latter problem we obtain an approximate solution for moving boundary function on specific time. Furthermore, we show the path of moving boundary from initial state to final state.