Complutense University Library

On the approximate controllability of some semilinear parabolic boundary-value problems

Díaz Díaz, Jesús Ildefonso and Henry, J. and Ramos del Olmo, Ángel Manuel (1998) On the approximate controllability of some semilinear parabolic boundary-value problems. Applied mathematics and optimization, 37 (1). pp. 71-97. ISSN 0095-4616

[img] PDF
Restricted to Repository staff only until 31 December 2020.

256kB

Official URL: http://www.springerlink.com/content/8b88rvgkhuyhn45c/fulltext.pdf

View download statistics for this eprint

==>>> Export to other formats

Abstract

We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem.


Item Type:Article
Uncontrolled Keywords:approximate controllability; semilinear parabolic boundary-value problems; interior or boundary controls; heat-equation
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15696
References:

Aubin, J.P. (1984) L’analyse non linéaire et ses motivations économiques. Masson, Paris.

Aubin, J.P., and Ekeland, I. (1984) Applied Nonlinear Analysis. Wiley-Interscience, New York.

Barbu, V. (1976) Nonlinear Semigroups and Differential Equations in Banach Spaces. Noordhoff, Leydon.

Benilan, Ph. (1978) Operateurs accretifs et semi-groupes dans les espaces L p (1 • p • 1). In: Functional Analysis and Numerical Analysis, H. Fujita (ed.). Japan Society for the Promotion of Science, pp. 15–53.

Brézis, H. (1973) Operateurs Maximaux Monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland, Amsterdam.

Díaz, J.I. (1991) Sur la contrôlabilité approchée des inéquations varationnelles et d’autres problèmes paraboliques non lin´eaires. C. R. Acad. Sci. Paris Ser I, 312:519–522.

Díaz, J.I. (1993) Approximate controllability for some nonlinear parabolic problems. In: System Modelling and Optimization. Proceedings of the 16th IFIP-TC7 conference, Compiegne (France). Lecture Notes in Control and Information Sciences. Springer-Verlag, Berlin.

Díaz, J.I. (1993) Mathematical analysis of some diffusive energy balance models in climatology. In:Mathematics, Climate and Environment, J.I. Díaz and J.L. Lions (eds.). Masson, Paris.

Díaz, J.I. (1994) Controllability and obstruction for some nonlinear parabolic problems in climatology.In: Modelado de Sistemas en Oceanografía, Climatología y Ciencias Mediambientales: aspectos matemáticos y numéricos, Málaga, 24–26 Enero, 1994, A. Valle and C. Pares (eds.). pp. 43–57.

Díaz, J.I., and Fursikov, A.V. (1994) A simple proof of the controllability from the interior for nonlinear parabolic problems. Appl. Math. Lett., 7(5):85–87.

Díaz, J.I., and Ramos, A.M. (1993) Resultados positivos y negativos sobre la controlabilidad aproximada de problemas parabólicos semilineales. Proceedings of XIII C.E.D.Y.A./III Congreso de Matemática Aplicada, Univ. Politécnica of Madrid, September, 1993, A.C. Casal, L. Gavete, C. Conde, and J. Herranz (eds.). pp. 640–645.

Díaz, J.I., and Ramos, A.M. (1995) Positive and negative approximate controllability results for semilinear parabolic equations. Rev. Real Acad. Cienc. Madrid, LXXXIX(1-2):11–30.

Fabre, C., Puel, J.P., and Zuazua, E. (1992) Contrôlabilité approchée de l’équation de la chaleur semilinéaire. C. R. Acad. Sci. Paris Ser. I, 315:807–812.

Fabre, C., Puel, J.P., and Zuazua, E. (1995) Approximate controllability of the semilinear heat equation.Proc. Roy. Soc. Edinburgh, Sect. A, 125:31–61.

Friedman, A. (1964) Partial Differential Equations of Parabolic Type. Prentice-Hall, Englewood Cliffs, NJ.

Henry, J. (1978) Etude de la contrôlabilité de certaines équations paraboliques. Thèse d’Etat, Université Paris VI.

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

Lions, J.L. (1990) Remarques sur la contrôlabilité approchée. Proceedings of “Jornadas Hispano–Francesas sobre Control de Sistemas Distribuidos”. Universidad de Malaga, pp. 77–88.

Lions, J.L., and Magenes, E. (1968) Problèmes aux limites non homogènes et applications,Vol. 1. Dunod,Paris.

Mizohata, S. (1958) Unicité du prolongement des solutions pour quelques opérateurs différentiels paraboliques. Mem. Coll. Sci. Univ. Kyoto, Ser. A, 31(3):219–239.

Saut, J.C., and Scheurer, B. (1987) Unique continuation for some evolution equations. J. Differential Equations, 66:118–139.

Simon, J. (1987) Compact sets in the space L p.0; T I B/. Ann. Mat. Pura Appl. (4), 146:65–96.

Zuazua, E. (1991) Exact boundary controllability for the semilinear wave equation. In:Nonlinear Differential Equations and Their Applications, H. Brezis and J.L. Lions (eds.).Séminaire du Collège de France 1987–1988, Vol. X. Research Notes in Mathematics. Pitman, London, pp. 357–391.

Deposited On:20 Jun 2012 08:58
Last Modified:06 Feb 2014 10:30

Repository Staff Only: item control page