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.
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Ali Vahidian Kamyad received his BS from Ferdowsi University of Mashhad, Iran, and his MS from Institute of Mathematics Tehran, Iran and Ph.D at Leeds University, Leeds, England under the direction of J. E. Rubio. Since 1972 he has been at Ferdowsi University of Mashhad, he is a full professor and his research interests are mainly on optimal control of distributed parameter systems and applications of Fuzzy theory.
Hadi Basirzadeh received his BS from Shahid Chamran University of Ahvaz and his MS from Sistan and Baluchestan University, Iran and Ph.D at Ferdowsi University, Mashhad, Iran under the direction of A. V. Kamyad. Since 1992 he has been at Shahid Chamran University of Ahvaz, Iran, he is an assistant professor and his research interests are mainly on O.R, optimal control and applications of Fuzzy theory.
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Basirzadeh, H., Kamyad, A.V. An approach for solving of a moving boundary problem. JAMC 14, 97–113 (2004). https://doi.org/10.1007/BF02936101
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DOI: https://doi.org/10.1007/BF02936101