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Abstract:

We obtain results on local controllability (near an equilibrium point) for a nonlinear wave equation, by application of an infinite-dimensional analogue of the Lee-Markus method of linearization. Controllability of the linearized equation is studied by application of results of Russell, and local controllability of the nonlinear equation follows from the inverse function theorem. We prove that every state that is sufficiently small in a sense made precise in the paper can be reached from the origin in a time T depending on the coefficients of the equation. © 1975 Springer-Verlag New York Inc.

Registro:

Documento: Artículo
Título:Local controllability of a nonlinear wave equation
Autor:Fattorini, H.O.
Filiación:Departamento de Matemática Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Ciudad Universitaria, Buenos Aires, Argentina
Department of Mathematics, University of California, Los Angeles, 90024, California, United States
Año:1975
Volumen:9
Número:1
Página de inicio:30
Página de fin:45
DOI: http://dx.doi.org/10.1007/BF01698123
Título revista:Mathematical Systems Theory
Título revista abreviado:Math. Systems Theory
ISSN:00255661
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255661_v9_n1_p30_Fattorini

Referencias:

  • Ames, W.F., Discontinuity formation in solutions of homogenous non-linear hyperbolic equations possessing smooth initial data (1970) Internat. J. Non-Linear Mech., 5, pp. 413-428
  • Bellman, R., (1953) Stability Theory of Differential Equations, , McGraw-Hill, New York
  • Cirinà, M., Boundary controllability of nonlinear hyperbolic systems (1969) SIAM Journal on Control, 7, pp. 198-212
  • Dieudonné, J., (1960) Foundations of Modern Analysis, , Academic Press, New York
  • Ficken, F.A., Fleishman, B.A., Initial-value problems and time-periodic solutions for a nonlinear wave equation (1957) Communications on Pure and Applied Mathematics, 10, pp. 331-356
  • Lee, E.B., Markus, L., Optimal control for nonlinear processes (1961) Arch. Rat. Mech. Anal., 8, pp. 36-58
  • Lee, E.B., Markus, L., (1967) Foundations of Optimal Control Theory, , Wiley, New York
  • Lions, J.L., Magenes, E., (1968) Problèmes aux Limites non homogènes et Applications, Vol. I, , Dunod, Paris
  • Lions, J.L., Magenes, E., (1968) Problèmes aux Limites non homogènes et Applications, Vol. II, , Dunod, Paris
  • Lions, J.L., (1969) Quelques Methodes de Résolution des Problèmes aux Limites non linéaires, , Dunod-Gauthier-Villars, Paris
  • Riesz, F., Sz.-Nagy, B., (1955) Leçons d'Analyse Fonctionnelle, , 3ème éd., Akadémiai Kiadó, Budapest
  • Russell, D.L., Nonharmonic Fourier series in the control theory of distributed parameter systems (1967) J. Math. Anal. Appl., 18, pp. 542-560
  • Schwarz, L., (1959) Etude des Sommes d'Exponentielles, , 2ème éd., Hermann, Paris
  • Tricomi, F., (1953) Equazioni Differenziali, , Einaudi, Torino

Citas:

---------- APA ----------
(1975) . Local controllability of a nonlinear wave equation. Mathematical Systems Theory, 9(1), 30-45.
http://dx.doi.org/10.1007/BF01698123
---------- CHICAGO ----------
Fattorini, H.O. "Local controllability of a nonlinear wave equation" . Mathematical Systems Theory 9, no. 1 (1975) : 30-45.
http://dx.doi.org/10.1007/BF01698123
---------- MLA ----------
Fattorini, H.O. "Local controllability of a nonlinear wave equation" . Mathematical Systems Theory, vol. 9, no. 1, 1975, pp. 30-45.
http://dx.doi.org/10.1007/BF01698123
---------- VANCOUVER ----------
Fattorini, H.O. Local controllability of a nonlinear wave equation. Math. Systems Theory. 1975;9(1):30-45.
http://dx.doi.org/10.1007/BF01698123