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Obstruction and some approximate controllability results for the burgers equation and related problems

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Díaz Díaz, Jesús Ildefonso (1996) Obstruction and some approximate controllability results for the burgers equation and related problems. In Control of Partial Differential Equations and Applications. Lecture notes in pure and applied mathematics (174). Marcel Dekker, NEW YORK, pp. 63-76. ISBN 0-8247-9607-1

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Resumen

The paper studies the approximate controllability for the Burgers equation. Due to the presence of a superlinear term, an obstruction phenomenon arises which implies a lack of approximate controllability in spaces of type L^p or $C$. However, the author is able to prove several controllability results under suitable constraints on the desired state. Finally, a necessary condition for the approximate controllability of the Navier-Stokes system on a rectangle is given.


Tipo de documento:Sección de libro
Información Adicional:

IFIP TC7/WG-7.2 Conference on Control of Partial Differential Equations and Applications. LAREDO, SPAIN. 1994

Palabras clave:approximate controllability; Burgers equation; Navier-Stokes system
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:15864
Referencias:

Alt, H.W. and Luckhaus, S. (1983). Quasilinear Elliptic-Parabolic Differential Equations, Math. Z. 183, pp.311-341

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

Bandle, C. and Marcus, M. (1992). "Large" solutions of semilinear elliptic equations: existence, uniqueness and assymptotic behaviour, Journal d'Analyse Math. 58, pp. 9-24

Bandle, C., Díaz, G. and Díaz, J.I. (1994). Solutions d'équations de réaction-diffusion nonlinéaires explosant au bord parabolique, C.R.Aca. Sciences. París, 318, Serie I, pp. 455-460

Benilan, Ph. (1981). evolution equations and accretive operators, Lecture Notes, Univ. of Kentucky, Lexington.

Bernis, F., Díaz, J.I. and Ramos, A. (1995). Obstruction and approximate controllabillity results for higher order semilinear parabolic equations. Manuscript.

Brezis, H. (1973). Opérateurs maximaux monotones et semigroups de contractions dans les spaces de Hilbert. North Holland, Amsterdam.

Carrillo, J.(1986). Unicité des solutions du type Kruskov por des problémes elliptiques avec des terms de transport non lineaires. C.R.Aca. Sciences. París, 303, Serie I, pp 189-1992.

Díaz, G. and Letelier, R. (1983). Explosive solutions of quasilear elliptic equations: existence and uniqueness, Nonlinear Analysis, T.M.A 20, pp.97-125.

Díaz, J.I. (1991a). Sur la contrôllabilité approchée des inéquations variatonelles et d'autres problémes non-linéaires. C.R.Aca. Sciences. París, 312, Serie I, pp.519-522.

Díaz, J.I. (1991b). Sobre la controlabilidad aproximada de problemas no lineales disipativos. In the proceedings of Jornadas Hispano-Francesas sobre Control de Sistemas Distribuidos (A. Valle ed.). Univ. de Málaga. pp. 41-48.

Díaz, J.I. (1993a). Mathematical analysis of some diffusive energy balance models in Cimatology. In Mathematics, Climate and Environment, J.I. Díaz and J. L. Lions (eds.) Masson, pp. 28-56.

Díaz, J.I. (1993b). Approximate controllability for some simple nonlinear parabolic problems. Proceedings of 16 IFIP-TC7 conference on "System Modelling and Optimizacion", Compiegne (France), 5-9 July 1993. Lecture Notes in Control and Information Sciences. Springer-Verlag.

Díaz, J.I. (1994a). On the controllability of some simple climate models. In environment, Economics and their Mathematical models, J.I. Díaz and J. L. Lions (eds.) Masson,, pp. 29-44.

Díaz, J.I. (1994b). Controllability and Obstructions for some nonlinear parabolic problems in Climatology. In Modelado de Sistemas en Oceoanografía. (A. Valle and C. Pares eds.) Universidad de Málaga, pp. 43-58.

Díaz, J.I. and de Thelin, F. (1994). On a nonlinear parabolic problem arising in some models related to turbulent flows. SIAM J. Math. Anal. 25, pp. 1085-1111.

Díaz, J.I. and Ramos, A. M. (1993). Resultados positivos y negativos sobre la controlabilidad aproximada de problemas parábolicos semilineales. Actas de XIIICEDYA/III Congresos de Matemática Aplicada. Madrid.

Díaz, J.I. and Ramos, A. M. (1994). Positive and Negative approximate controllabilyty results for semilnear problems. Submitted.

El Badia, A. and Ain Seba, B. (1992). Contrôllabilité exacte de l'équation de Burgers,C.R.Aca. Sciences. París, 314, Serie I, pp. 373-378.

Fabré, C. Puel, J. P. and Zuazua, E. (1992a). Contrôllabilité approcheée de l'équation de la chaleur semilinéaire, C.R.Aca. Sciences. París, 315, Serie I, pp. 807-812

Fabré, C. Puel, J. P. and Zuazua, E. (1992b). Approximate contolability of the semilinear heat equations. IMA Preprint Series, Minnesota.

Fursikov, A. V. and Imanuvilov, O. Y. (1993a). On approximate controllability of the Stokes system, Annales de la Faculté des Sciences de Toulouse, Vol II nº2, pp. 205-232.

Fursikov, A. V. and Imanuvilov, O. Y. (1993b). On controllabity of certain systems simulating a fluid flow. Manuscript.

Gagneux, G. and Madaune.Tort, M (1994). Unicité des solutions faibles d'équations de diffusion-convection. C.R.Aca. Sciences. París, 318, Serie I, pp.919-924.

Gilbarg, D. and Trudinger, N. S. (1977). Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin.

Glowinski, R. and Lions, J. L.(1994). Exact and Approximate Controllability for Distributed Parameter Systems. Manuscript.

henry, J. (1978). etude de la contrôlabilté de certains équations paraboliques. Thése d'Etat. Université de Paris VI.

Lin, F. H. (1991). Nodal sets of solutions of elliptic and parabolic equations. Comm. in Pure and Appl. Math. 44, pp. 287-308.

Lions, J.L. (1968). Contôle Optimal Systems Gouvernés par les Equations Derivées Partielles. Dunod, Paris.

Lions, J.L. (1990). Are there connections between turbulence and controllability?. Lect. Notes 144. Springer-Verlarg(A. Bensoussan and J.L.Lions eds.)

Lions, J.L. (1992). Remarks on approximate controllability, J. Analyse Math. 59, pp. 103-116.

Sault, J.C. and Scheurer, B.(1987). Unique continuation for some evolution equations. J. Diff. Equations, 66, pp. 118-139.

Simon, J. (1987). Compact sets in the space L p (0,T:B), Annali di Matematica Pura ed Applicata, CXLVI, pp. 65-96.

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