Publication: On the approximate controllability for higher order parabolic nonlinear equations of Cahn-Hilliard type
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1998
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Birhäuser
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Abstract
Sire prove the approximate controllability property for some higher order parabolic nonlinear equations of Cahn-Hilliard type when the nonlinearity is of sublinear type at infinity. We also give a counterexample showing that this property may fail when the nonlinearity is of superlinear type.
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International conference on control and estimation of distributed parameter systems (1996. Vorau, Austria)
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Aubin, J.P.: Un théorème de compacité. C. R. Acad. Sci., Paris, Serie I, T. 256, pp. 5042-5044, (1963).
Aubin, J.P.: L'analyse non linéaire et ses motivations économiques. Masson. (1984).
Aubin, J.P. and Ekeland, I.: Applied nonlinear Analysis. Wiley-Interscience Publication, New York, (1984).
Bernis, F.: Elliptic and Parabolic Semilinear Problems without Conditions at infnity. Arch. Rat. Mech. Anal., Vol. 106, N. 3, pp. 217-241, (1989).
Brézis, H.:Analyse Fonctionnelle: Théorie et applications. Masson, Paris, (1987).
Cahn, J.W. and Hilliard, J.E.: Free energy of a nonuniform system. I. Interfacial free energy. J.Chem. Phys. N. 28, pp. 258-267, (1958).
Díaz, J.I. and Ramos, A.M.: Positive and negative approximate controllability results for semilinear parabolic equations. To appear in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales,Madrid, (1997).
Elliot, C.M. and Songmu, Z.: On the Cahn-Hilliard Equation. Arch. Rat. Mech. Anal. N. 96, pp.339-357, (1986).
Fabre, C., Puel, J.P. and Zuazua, E.: Contrôlabilité approchée de l'équation de la chaleur semi-linéaire. C. R. Acad. Sci. Paris, t. 315, Série I, pp. 807-812, (1992).
Fabre, C., Puel, J.P. and Zuazua, E.: Approximate controllability of the semilinear heat equation,Proceedings of the Royal Society of Edinburgh, 125A, pp. 31-61, (1995).
Haraux, A.: Nonlinear Evolution Equations. Lecture Notes in Mathematics. Springer-Verlag, Heidelberg, (1981).
Lions, J.L.: Contrôle optimal de systemes gouvernés par des equations aux derivées partielles. Dunod,Paris, (1968).
Lions, J.L.: Quelques méthodes de résolution des probléms aux limites non lin¶eares. Dunod, Paris,(1969).
Lions, J.L.: Remarques sur la contrôlabilité approchée. In Proceedings of Jornadas Hispano-Francesas sobre Control de Sistemas Distribuidos, Universidad de Malaga, pp. 77-88, (1990).
Lions, J.L. and Magenes, E.: Problèmes aux limites non homogènes et applications, Vol. 1, Dunod, Paris, (1968).
Lions, J.L. and Magenes, E.: Problèmes aux limites non homogènes et applications, Vol. 2, Dunod, Paris, (1968).
Saut, J.C. and Scheurer, B.: Unique continuation for some evolution equations. J. Differential Equations, Vol. 66, N. 1, pp. 118-139, (1987).
Simon, J.: Compact Sets in the Space Lp(0; T;B). Annali di Matematica Pura ed Applicata. Serie 4,N. 146, pp.65-96, (1987).