Geodesic
Modeling and optimization of melting and solidification process
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2004), pp. 91-109.

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An optimal control problem is considered for two-phase Stefan problem describing the process of melting and solidification. The problem is solved numerically by variation and finite-difference methods. The results are described and analyzed in detail. Some of them are presented as tables and plots. 
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A. F. Albou; V. I. Zubov. Modeling and optimization of melting and solidification process. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2004), pp. 91-109. https://geodesic-test.mathdoc.fr/item/BASM_2004_3_a8/

[1] Lions J.-L., Controle optimal de systemes gouvernes par des equations au derivees partielles, Gauthier-Villars, Paris, 1968 ; Mir, Moscow, 1972 | MR | Zbl

[2] Lur'e K. A., Optimal Control in Problems of Mathematical Physics, Nauka, Moscow, 1975 (in Russian) | MR

[3] Ahmed N. U., Teo K. L., Optimal Control of Distributed Parameter Systems, North Holland, New York, 1981 | MR | Zbl

[4] Vasil'ev F. P., Optimization Methods, Faktorial, Moscow, 2002 (in Russian)

[5] Yurii A. D., “An Optimal Stefan-Type Problem”, Dokl. Akad. Nauk SSSR, 251 (1980), 1317–1321 | MR

[6] Gol'dman N. L., Inverse Stefan Problems: Theory and Solution Methods, Mosk. Gos. Univ., Moscow, 1999 (in Russian)

[7] Rose M. E., “A Method for Calculating Solutions of Parabolic Equations with a Free Boundary”, Math. Comput., 14 (1960), 249–256 | DOI | MR | Zbl

[8] White R. E., “An Enthalpy Formulation of the Stephan Problem”, SIAM J. Numer. Anal., 19 (1982), 1129–1157 | DOI | MR | Zbl

[9] White R. E., “A Numerical Solution of the Enthalpy Formulation of the Stephan Problem”, SIAM J. Numer. Anal., 19 (1982), 1158–1172 | DOI | MR | Zbl

[10] Albu A. F., Zubov V. I., “Modified Scheme for Analyzing the Process of Melting”, Zh. Vychisl. Mat. Mat. Fiz., 41 (2001), 1434–1443 | Zbl

[11] Evtushenko Y. G., “Computation of Exact Gradients in Distributed Dynamic Systems”, Optimizat. Methods and Software, 9 (1998), 45–75 | DOI | MR | Zbl

[12] Albu A. F., Gorbunov V. I., Zubov V. I., “Optimal Control of the Process of Melting”, Zh. Vychisl. Mat. Mat. Fiz., 40 (2000), 517–531 | MR | Zbl

[13] Albu A. F., Zubov V. I., “Optimal Control of the Process of Solidification”, Zh. Vychisl. Mat. Mat. Fiz., 44 (2004), 38–50 | MR | Zbl