Global steady-state controllability of one-dimensional semilinear heat equations

SIAM Journal on Control and Optimization

Volumn 43, Issue 2, 2005, Pages 549-569

  Coron, Jean Michel ^a   Trélat, Emmanuel ^a  

^a Universitè de Paris Sud   (France)

Author keywords

Controllability; Heat equation; Lyapunov functional; Pole shifting

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; CONTROL SYSTEMS; DATA ACQUISITION; EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; PROBLEM SOLVING;

BOUNDARY CONTROLLABILITY; HEAT EQUATIONS; LYAPUNOV FUNCTIONAL; POLE SHIFTING;

CONTROLLABILITY;

EID: 16244411105     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S036301290342471X     Document Type: Article

References (18)

1. J. BEBERNES AND D. EBERLY, Mathematical Problems from Combustion Theory, Appl. Math. Sci. 83, Springer-Verlag, New York, 1989.
2. T. CAZENAVE AND A. HARAUX, Introduction aux problèmes d'évolution semi-linéaires, Math. Appl. 1, Ellipses, Paris, 1990.
3. J. M. CORON, Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations, ESAIM Control Optim. Calc. Var., 8 (2002), pp. 513-554.
4. J. I. DIAZ, 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 Appl. Math. 174, Dekker, New York, 1996, pp. 63-76.
5. C. FABRE, J. P. PUEL, AND E. ZUAZUA, Approximate controllability of the semilinear heat equation, Proc. Roy. Soc. Edinburgh Sect. A, 125 (1995), pp. 31-61.
6. E. FERNÁNDEZ-CARA, Null controllability of the semilinear heat equation, ESAIM Control Optim. Calc. Var., 2 (1997), pp. 87-103.
7. E. FERNÁNDEZ-CARA AND E. ZUAZUA, Null and approximate controllability for weakly blowing up semilinear heat equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 17 (2000), pp. 583-616.
8. 1+α, J. Fac. Sci. Univ. Tokyo Sect. IA Math, 13 (1966), pp. 109-124.
9. A. FURSIKOV AND O. YU. IMANUVILOV, On controllability of certain systems simulating a fluid flow, in Flow Control, IMA Vol. Math. Appl. 68, M. D. Gunzburger, ed., Springer-Verlag, New York, 1995, pp. 149-184.
10. J. HENRY, Etude de la contrôlabilité de certaines équations paraboliques non linéaires, Thèse, Paris, 1977.
11. O. YU. IMANUVILOV, Controllability of parabolic equations, Mat. Sb. 186 (1995), pp. 879-900.
12. S. KAPLAN, On the growth of solutions of quasilinear parabolic equations, Comm. Pure Appl. Math., 16 (1963), pp. 305-330.
13. H. K. KHALIL, Nonlinear Systems, Macmillan, New York, 1992.
14. t = -Au + F(u), Arch. Ration. Mech. Anal., 51 (1973), pp. 371-386.
15. p-1u, Duke Math. J., 86 (1997), pp. 143-195.
16. M. REED AND B. SIMON, Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators, Academic Press, New York, London, 1978.
17. D. L. RUSSELL, Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions, SIAM Rev., 20 (1978), pp. 639-739.
18. H. ZAAG, A remark on the energy blow-up behavior for nonlinear heat equations, Duke Math. J., 103 (2000), pp. 545-555.