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

Applied Mathematics and Optimization

Volumn 37, Issue 1, 1998, Pages 71-97

  Diaz J I ^a   Henry, J ^b   Ramos, A M ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b INRIA   (France)

Author keywords

Approximate controllability; Interior or boundary controls; Semilinear parabolic boundary value problems

Indexed keywords

APPROXIMATION THEORY; CONTROLLABILITY; NONLINEAR EQUATIONS;

APPROXIMATE CONTROLLABILITY; CANCELLATION METHOD; KAKUTANI FIXED POINT THEOREM;

BOUNDARY VALUE PROBLEMS;

EID: 0031703704     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002459900069     Document Type: Article

References (23)

1. Aubin, J.P. (1984) L'analyse non linéaire et ses motivations économiques. Masson, Paris.
2. Aubin, J.P., and Ekeland, I. (1984) Applied Nonlinear Analysis. Wiley-Interscience, New York.
3. Barbu, V. (1976) Nonlinear Semigroups and Differential Equations in Banach Spaces. Noordhoff, Leydon.
4. p (1 ≤ p ≤ ∞). In: Functional Analysis and Numerical Analysis, H. Fujita (ed.). Japan Society for the Promotion of Science, pp. 15-53.
5. Brézis, H. (1973) Operateurs Maximaux Monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland, Amsterdam.
6. Díaz, J.I. (1991) Sur la contrôlabilité approchée des inéquations varationnelles et d'autres problèmes paraboliques non linéaires. C. R. Acad. Sci. Paris Ser I, 312:519-522.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
15. Friedman, A. (1964) Partial Differential Equations of Parabolic Type. Prentice-Hall, Englewood Cliffs, NJ.
16. Henry, J. (1978) Etude de la contrôlabilité de certaines équations paraboliques. Thèse d'Etat, Université Pans VI.
17. Lions, J.L. (1968) Contrôle optimal de systèmes gouvernés par des équations aux derivées partielles. Dunod, Paris.
18. Lions, J.L. (1990) Remarques sur la contrôlabilité approchée. Proceedings of "Jornadas HispanoFrancesas sobre Control de Sistemas Distribuidos". Universidad de Malaga, pp. 77-88.
19. Lions, J.L., and Magenes, E. (1968) Problèmes aux limites non homogènes et applications, Vol. 1. Dunod, Paris.
20. Mizohata, S. (1958) Unicité du prolongement des solutions pour quelques opérateurs différentiels paraboliques. Mem. Coll. Sci. Univ. Kyoto, Ser. A, 31(3):219-239.
21. Saut, J.C., and Scheurer, B. (1987) Unique continuation for some evolution equations. J. Differential Equations, 66:118-139.
22. p(0, T; B). Ann. Mat. Pura Appl. (4), 146:65-96.
23. 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.