Tytuł artykułu
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Warianty tytułu
Języki publikacji
Abstrakty
This paper presents a mathematical model for a chemical process used to machine cristal as glass or silica. A short physical description is presented from which we draw the mathematical model. We obtain a coupled parabolic equations system on a free boundary domain with a non-linear condition on the boundary. The existence and the uniqueness is proved in the one-dimensional case.
Wydawca
Czasopismo
Rocznik
Tom
Strony
35--58
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
- Département De Mathématiques Appliquées Université Blaise Pascal 63177 Aubiére Cedex, clain@ucfma.univ-bpclermont.fr
Bibliografia
- [1] Born, H.H., Prigogine, M., The rate equation for the dissolution of silica in hydrochloric-hydrofluoric acid mixture, Journal de Chimie Physique 76(6) (1979), 538-544.
- [2] Bruch, J.C., Papadopoulos, C.A., Sloss, J.M., Parallel computing using in solving wet chemical etching semiconductor fabrication problems, GATUKO Internat. Ser. Math. Sci. Appl. 1 (1993), 281-292.
- [3] Brezis, H., Analyse Fonctionnelle, Théorie et Applications, Masson, 1987.
- [4] Buck, R.C., Advanced Calculus, 2nd Edition, Internat. Ser. Pure Appl. Math., Me Graw-Hill, New York, 1965.
- [5] Čermák, L., Finite element solution of diffusion problems with a moving boundary in semiconductor device technology, Pitman Res. Notes Math. Ser. 186 (1990), 621-627.
- [6] Cuvelier, C., Vuik, C., Numerical solution of an etching problem, J. Comput. Phys. 59 (1985), 247-263.
- [7] Fripiat, J.J., Prigogine, M., La réactivité des surfaces de silices, Journal de Chimie Physique 76(1) (1979), 26-34.
- [8] Judge, J.S., The etching of thin film dielectric materials, J. Electrochem. Soc. 118 (1971), 19-36.
- [9] Kuiken, H.K., Mathematical modelling of etching processes, Pitman Res. Notes in Math. Ser. 185 (1990), 89-109.
- [10] Ladyshenskaya, O., Solonnikov, V., Uraltseva, N., Linear and Quasi-Linear Equations of Parabolic Type (English translation), Transi. Math. Monograph., Amer. Math. Soc. 23, Providence, R.I., 1968.
- [11] Simon, J., Compacts sets in the spaces Lp(0,T;B), Ann. Mat. Pura Appl. 146(4) (1987), 65-96.
- [12] Stampacchia, G., Équations Elliptiques du Second Ordre à Coefficients Discontinues, Les Presses Universitaires de Montréal, 1965.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0012-0028
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