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Approximate controllability and obstruction phenomena for quasilinear diffusion equations

Díaz Díaz, Jesús Ildefonso and Ramos del Olmo, Ángel Manuel (1997) Approximate controllability and obstruction phenomena for quasilinear diffusion equations. In Computational Science for the 21st Century. John Wiley & Sons., Chichester , pp. 698-707. ISBN 0-471-97298-3

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Item Type:Book Section
Additional Information:

Symposium on Computational Science for the 21st-Century, Honoring Roland Glowinski on the Occasion of His 60th Birthday. Tours, MAY 05-07, 1997

Uncontrolled Keywords:approximate controllability; nonlinear diffusion equations; obstruction phenomena
Subjects:Sciences > Mathematics > Differential geometry
ID Code:15823
References:

Aubin, J.P. (1963) Un théoréme de compacité. C. R. Acad. Sci., Paris, Serie 1, T. 256. pp. 5042-5044.

Bandle, C. and Markus, M. (1992) "Large" solutiolls of semi linear elliptic equations: existence, uniqueness and asymptotic behaviour. Journal d'Analyse Mathématique, 58, pp. 9-24.

Benilan, Ph. and Crandall, M.G. (1981) The continuous dependence on  of solutions of u t-- (u) = O. Indiana Univ. Math. J., 30, pp. 161-177.

Brézis, H. (1971) Monotonicity metbods in Hilbert spaces and some applications to nonlinear partial differential equations. In Nonlinear Func.tional Analy.sis. (E. Zarantonello ed.), Academic Press, New York, pp. 101-156.

Brézis, H. (1973) Operateurs Maximus Monotones el Semigroupes de Contractions dans les Espaces de Hilbert. North-Holland, Amsterdam.

Carthel, C., Glowinski, R. and Lions J.L. (1994) On Exact and Approximate Boundary Controllability for the Heat Equation: A numericaJ Approach. Journal of Optimization Theory and Applications. 82, n. 3, pp. 424-486

Díaz, J.L. (1986) Elliptic and Parabolic Quasilinear Equations Giving Rise to a Free Boundary. In Nonlinear Funtional Analysis and its Applications, Proceedings of Symposia in Pure Mathematics, Vol. 45 /F.E. Browder ed.), AMS Providence, pp.381-393.

Díaz, J.L. (1991) Sur la contrôlabilité approchée des inequations variationelles et d'autres problèmes paraboliques non-linéaires. C.R. Acad. Sci. de Paris, 312) Serie I, pp. 519-522.

Díaz, J.L. (1994) Controllability and Obstruction for some nonlinear parabolic problems in Climatology. In Modelado de Sistemas en Oceanografía, Climatología y Ciencias Medioambientales: aspectos matemáticos y numéricos. (A. Valle a.nd C. Pares eds.), Univ. de Málaga, pp. 43-57.

Díaz, J.L. (1995a) Approximate controllability for some non1inear parabolic problems. In System Modelling and Optimization. (J. Henry and J.P. Yvon eds.), Springer-Verlag, London, pp. 128-143.

Díaz, J.L. (1995b) Obstruction and some Approximate Controllability Results for the Burges Equation and Related Problems. In Control of Partial Differential Equations and Applications. (E. Casas ed.), Marcel Dekker, Inc., New York, pp. 63-76.

Díaz, J.L. and Fursikov, A.V. (1994) A simple proof of the approximate controllability from the interior for nonlinear evolution problems. Applied Math. Letters. 7, pp. 85-87.

Díaz, J.L.. and Ramos. A.M. (1994) Resultados positivos y negativos sobre la controlabildad aproximada de problemas parabólicos semilineales. In Proceedings of III Congreso de Matemática Aplicada; XIII C.E.D.Y.A. (A.C. Casal et al. eds.). Uniy. Politécnica de Madrid, pp. 640-645.

Díaz, J.L.. and Ramos, A.M. (1997a) Positive and negative approximate controllability results for semilinear parabolic equations. To appear in Revista de la Real Academia de Ciencias Exactas, Física y Naturales, Madrid.

Díaz, J.L. and Ramos. A.M. (1997b) On tbe Approximate Controllability for Higher Order Parabolic Nonlinear EquationS of Cahn-Hilliard Type. To appear in Proceedings of the International Conference on Control and Estimation of distributed Parameter Systems. Vorau (Austria).

Fabre, C. Puel, J.P. and Zuazua, E.(1992)Contrôlabilité approchée de l'équation de la chaleur semilinéaire. C.R.Acad.Scí. París,T.315,Série I, pp. 807-812.

Fabre, C. Puel, J.P. and Zuazua, E. (1995) Approximate controllability of the semilinear heat equation,Proceedings of the Royal Society of Edinburgh, 125A, pp. 31-61.

Glowinski. R. and Lions, J.L. (1994) Exact aud Approximate Controllability for Distributed Parameter Systems. Part 1, Acta Numerica, I pp. 269-378.

Glowinski. R. and Lions J.L (I995) Exact and Approximate Controllability for Distributed Parameter Systems. Part II. Acta Numerica, 2, pp. 1-175.

Henry, J. (1978) Contrôle d'un Réacteur Enzymatique à l’Aide de Modèles à Paramètres Distribués. Quelques Problèmes de Contrôlabilité de Systèmes Paraboliques. Thèse d'Etat, Université Paris VI.

Herrero, M.A. and Pierre, M. (1985) The Cauchy Problem for Ut = u when O < m < 1. Trans. Amer. Math. Soc., 291, pp. 145-158.

Kalashnikov. A.S. (1987) Some problems of the qualitative theory of nonlinear degenerate second-order parabolic equations. Russ. Math. Survs .. 42, pp. 169-222 .

Lions, J.L. (1968) Contrôle optimal de systèmes gouvernés par des équations aux derives partielles. Dunod.

Lions, J.L. (1990) Remarques sur la contrôlabilité approchée. In Proceecüngs of Jornadas Hispano-Francesas sobre Control de Sistemas Distribuidos, Univ. de Malaga, pp. 77-88.

Peletier, L.A. (1981) The porous medium equation. In Application oj Nonlinear Analysis in the Phisical Sciences. (H. Amann et al. eds.), Pitman, London, pp. 229-241.

Russell. D. L. (1978) Controllability and Stabilizability Theory for Linear Partial Dilferential Equations. Recent Progress and Open Questions. SIAM Review, 20, pp. 639-739.

Saut, J.C. and Scheurer, B. (1987) Unique continuation for some evolution equations. J. Differential Equations, Vol. 66, N. 1, pp. 118-139.

Vázquez, J.L. (1992) An introduction to the Mathematical Theory of the Porous, Medium Equation. In Shape Optimization and Free Boundaries.(M.C. Delfour ed.),Kluwer Acad. Publ., Dordrecht, pp. 347-389.

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