Approximate controllability for some nonlinear parabolic problems

1. C. Bandle, G. Díaz et J.I. Díaz: Solutions d'equations de réaction-diffusion non-linéaires, explosant au bord parabolique. To appear in C.R.Acad.Sci. de Paris.

   Google Scholar 

2. N. Carmichael and M.D. Quinn: Fixed point methods in nonlinear control. In Distributed Parameter System. F.Kappel et al. (eds.), Springer-Verlag (1985), 24–51.

   Google Scholar 

3. J.I. Díaz: Sur la contrôllabilité approchée des inéquations variationelles et d'autre problémes paraboliques non-linéaires. C.R.Acad.Sci. de Paris, 312, serie I, (1991), 519–522.

   MATH  Google Scholar 

4. J.I.Díaz: Sobre la controlabilidad aproximada de problemas no lineales disipativos. In Jornadas Hispano-Francesas sobre Control de Sistemas Distribuidos. Univ. Málaga (1991), 41–48.

   Google Scholar 

5. J.I.Díaz: On the controllability of some simple climate models. In Environment, Economics and their Mathematical Models. J.I. Díaz and J.L. Lions (eds.). Masson (1993).

   Google Scholar 

6. J.I.Díaz and A.V.Fursikov: A simple proof of the controllability from the interior for nonlinear evolution problems. Submitted.

   Google Scholar 

7. J.I.Díaz and A.V.Fursikov: Approximate controllability of the Stokes system by external local one-dimensional forces. Manuscrit.

   Google Scholar 

8. J.I.Díaz, J.Henry and A.M.Ramos: Article in preparation.

   Google Scholar 

9. J.I.Díaz and J.Hernández: Qualitative properties of free boundaries for some nonlinear degenerate parabolic equations. In Nonlinear Parabolic Equations: Qualitative Properties of Solutions. L.Boccardo and A. Tesei (eds.). Pitman (1987), 85–93.

   Google Scholar 

10. J.I.Díaz and A.M.Ramos: Positive and negative approximate controllability results for semilinear problems. In Actas del XIII CEDYA. Univ. Politécnica de Madrid (1994).

    Google Scholar 

11. A. El Badia and B. Ain Seba: Contrôlabilité exacte de l'équation de Burger. C.R.Acad. Sci. de Paris, 314, serie I, (1992), 373–378.

    MATH  Google Scholar 

12. C. Fabré, J.P. Puel and E. Zuazua: Contrôlabilité approchée de l'équation de la chaleur. C.R.Acad. Sci. de Paris, 315, serie I, (1992), 807–812.

    MATH  Google Scholar 

13. C.Fabré, J.P. Puel and E.Zuazua: Approximate controllability of the semilinear heat equation. IMA Preprint Series, (1992).

    Google Scholar 

14. C. Fabré, J.P. Puel and E. Zuazua: Contrôlabilité approchée de l'équation de la chaleur linéaire avec des contrôles de norme L^∞ minimale. C.R.Acad. Sci. de Paris, 316, serie I, (1993), 679–684.

    MATH  Google Scholar 

15. E.Fernández-Cara and J.Real: On a conjeture due to J.L.Lions. To appear in Nonlinear Analysis. TMA.

    Google Scholar 

16. A.V. Fursikov and O.Y.Imanuvilov: On the approximate controllability of the Stokes systems. To appear in Annales de la Faculté des Sciences de Toulouse.

    Google Scholar 

17. A.V.Fursikov and O.Y.Imanuvilov: On the approximate controllability of certain systems simulating a fluid flow. Preprint (1993).

    Google Scholar 

18. Y. Ekeland and R. Temam: Analyse Convexe et Problémes Variationelles. Dunod, Gauthier-Villars, (1974).

    Google Scholar 

19. J.Henry: Etude de la contrôlabilité de certains équations paraboliques. Thèse d'Etat, Université Paris VI (1978).

    Google Scholar 

20. A.S. Kalsahnikov: Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations. Russ. Math. Survs. 42, (1987), 169–222.

    Article  Google Scholar 

21. S. Kamin, L.A. Peletier and J.L. Vázquez: Classification of singular solutions of a nonlinear heat equations. Duke Math. Jour., 58, (1989), 601–615.

    Article  MATH  Google Scholar 

22. J.L.Lions: Contrôle Optimal des Systems Gouvernés par des Equations aux Derivées Partielles. Dunod, (1968).

    Google Scholar 

23. J.L.Lions: Remarques sur la contrôlabilité approchée. In Jornadas Hispano-Francesas sobre Control de Sistemas Distribuidos. Univ. de Málaga, (1991), 77–88.

    Google Scholar 

24. J.L.Lions: Are there connections between turbulence and controllability?. In Analysis and Optimization des Systems. Lecture Notes in Control and Information Series 144, Springer-Verlag, (1990).

    Google Scholar 

25. J.L.Lions: Exact controllability for distributed systems. Some trends and some problems. In Applied and Industrial Mathematics. R.Sigler (ed.), Kluwer (1991), 59–84.

    Google Scholar 

26. J.L.Lions: Remarks on approximate controllability for parabolic systems. In Finite Elements in the 90's., E.Oñate et al. (eds.), Springer-Verlag, (1991), 612–620.

    Google Scholar 

27. J.L.Lions: Unpublished manuscrit.

    Google Scholar 

28. S. Mizohata: Unicité du prologment des solutions pour quelques opérateurs differentielles paraboliques. Mem.Coll. Sci.Univ.Kyoto, serie A31, (1958), 219–239.

    MathSciNet  Google Scholar 

29. K. Naito and T.I. Seidman: Invariance of the approximately reachable set under non-linear perturbations. SIAM J. Control and Optimization. 29, (1991), 731–750.

    Article  MATH  MathSciNet  Google Scholar 

30. D.L. Russell: Controllability and stabilizability theory for nonlinear partial differential equations: recents progress and open questions. SIAM Rev. 20, (1978), 639–739.

    Article  MATH  MathSciNet  Google Scholar 

31. J.C. Saut and B. Scheurer: Unique continuation for some evolution equations. J.Differenti Equations, 66, (1978), 118–139.

    Article  MathSciNet  Google Scholar 

32. T.I. Seidman: Invariance of the reachable set under nonlinear perturbations. SIAM J.Control and Optimizations, 25, (1987), 1173–1191.

    Article  MATH  MathSciNet  Google Scholar 

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