Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010
Spectral problems. Issue dedicated to the memory of M. Birman
Page(s) 4 - 31
DOI https://doi.org/10.1051/mmnp/20105401
Published online 12 May 2010
  1. S. A. Avdonin and B. P. Belinskiy, Controllability of a string under tension. Discrete and Continuous Dynamical Systems: A Supplement Volume, (2003), 57–67. [Google Scholar]
  2. S. A. Avdonin and B. P. Belinskiy, On the basis properties of the functions arising in the boundary control problem of a string with a variable tension. Discrete and Continuous Dynamical Systems: A Supplement Volume, (2005), 40–49. [Google Scholar]
  3. S. A. Avdonin and B. P. Belinskiy, On controllability of a rotating string. J. Math. Anal. Appl., 321 (2006), 198–212. [CrossRef] [MathSciNet] [Google Scholar]
  4. S. A. Avdonin, B. P. Belinskiy and S. A. Ivanov, On controllability of an elastic ring. Appl. Math. Optim., 60 (2009), 71–103. [CrossRef] [MathSciNet] [Google Scholar]
  5. S. A. Avdonin and S. A. Ivanov. Families of Exponentials. The Method of Moments in Controllability Problems for Distributed Parameter Systems. Cambridge University Press, New York, 1995. [Google Scholar]
  6. S. A. Avdonin and S. A. Ivanov, Exponential Riesz bases of subspaces and divided differences. St. Petersburg Mathematical Journal, 13 (2001), 339–351. [Google Scholar]
  7. S. Avdonin, S. Lenhart and V. Protopopescu, Solving the dynamical inverse problem for the Schrödinger equation by the Boundary Control method. Inverse Problems, 18 (2002), 41–57. [Google Scholar]
  8. S. Avdonin and W. Moran, Ingham type inequalities and Riesz bases of divided differences. Int. J. Appl. Math. Comput. Sci., 11 (2001), 101–118. [Google Scholar]
  9. S. A. Avdonin and W. Moran, Simultaneous control problems for systems of elastic strings and beams. Systems and Control Letters, 44 (2001), 147–155. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  10. S. A. Avdonin and M. Tucsnak, On the simultaneously reachable set of two strings. ESAIM: Control, Optimization and Calculus of Variations, 6 (2001), 259–273. [CrossRef] [EDP Sciences] [Google Scholar]
  11. V. Barbu and M. Iannelli, Approximate controllability of the heat equation with memory. Differential and Integral Equations, 13 (2000), 1393–1412. [MathSciNet] [Google Scholar]
  12. B. P. Belinskiy, J. P. Dauer, C. F. Martin and M. A. Shubov, On controllability of an elastic string with a viscous damping. Numerical Functional Anal. and Optimization, 19 (1998), 227–255. [CrossRef] [Google Scholar]
  13. M. I. Belishev, Canonical model of a dynamical system with boundary control in inverse problem for the heat equation. St. Petersburg Math. Journal, 7, (1996), 869–890. [Google Scholar]
  14. A. Erdélyi. Asymptotic Expansions. Dover Publications, Inc., 1956. [Google Scholar]
  15. I. C. Gohberg and M. G. Krein. Introduction to the Theory of Linear Nonselfadjoint Operators", Translations of Mathematical Monographs. American Mathematical Society. 18, Providence, RI, 1969. [Google Scholar]
  16. J. P. Den Hartog. Mechanical Vibrations. McGraw-Hill Book Company, New York, 1956. [Google Scholar]
  17. S. Hansen and E. Zuazua, Exact controllability and stabilization of a vibrating string with an interior point mass. SIAM J. Control Optim., 33 (1995), 1357–1391. [CrossRef] [MathSciNet] [Google Scholar]
  18. T. von Kàrmàn and M. A. Biot. Mathematical Methods in Engineering. McGraw-Hill Book Company, New York, 1940. [Google Scholar]
  19. O. A. Ladyzhenskaia. The Boundary Value Problems of Mathematical Physics. Springer-Verlag, New York, 1985. [Google Scholar]
  20. B. M. Levitan and I. S. Sargsjan. Sturm–Liouville and Dirac Operators. Translated from the Russian. Mathematics and its Applications (Soviet Series), 59. Kluwer Academic Publishers Group, Dordrecht, 1991. [Google Scholar]
  21. N. W. McLachlan. Theory and Applications of Mathieu Functions, Oxford, 1947. [Google Scholar]
  22. A. V. Metrikine and M. V. Tochilin, Steady-state vibrations of an elastic ring under moving load. J. Sound and Vibration, 232 (2000), 511–524. [CrossRef] [Google Scholar]
  23. L. Pandolfi, The controllability of the Gurtin-Pipkin equation: a cosine operator approach. Applied Mathematics and Optimization, 52 (2005), 143–165. [CrossRef] [MathSciNet] [Google Scholar]
  24. L. Pandolfi, Riesz system and the controllability of heat equations with memory. Integral Eq. Oper. Theory, 64 (2009), 429–453. [CrossRef] [Google Scholar]
  25. L. Pandolfi, Riesz systems, spectral controllability and an identification problem for heat equations with memory . Quaderni del Dipartimento di Matematica, Politecnico di Torino, “La Matematica e le sue Applicazioni”n. 6-2009 (in print, Discr. Cont. Dynam. Systems). [Google Scholar]
  26. L. Pandolfi, Riesz systems and moment method in the study of viscoelasticity in one space dimension. Quaderni del Dipartimento di Matematica, Politecnico di Torino, “La Matematica e le sue Applicazioni”n. 5-2009 (in print, Discr. Cont. Dynam. Systems). [Google Scholar]
  27. D. L. Russell, Nonharmonic Fourier series in the control theory of distributed parameter systems. J. Math. Anal. Appl., 18 (1967), 542–559. [CrossRef] [MathSciNet] [Google Scholar]
  28. D. L. Russell, Controllability and stabilizability theory for linear partial differential equations. SIAM Review, 20 (1978), 639–739. [CrossRef] [MathSciNet] [Google Scholar]
  29. D. L. Russell, On exponential bases for the Sobolev spaces over an interval. J. Math.Anal.Appl., 87 (1982), 528–550. [CrossRef] [MathSciNet] [Google Scholar]
  30. W. Soedel. Vibrations of Shells and Plates. Marcel Dekker, Inc., New York, 1993. [Google Scholar]
  31. M. E. Taylor. Pseudodifferential Operators. Princeton University Press, Princeton, NJ, 1981. [Google Scholar]
  32. S. Timoshenko. Thèorie des Vibrations. Libr. Polytecnique Ch Bèranger, Paris, 1947. [Google Scholar]
  33. V. Z. Vlasov. ObŽcaya Teoriya Obolocek i eë Prilođeniya v Tehnike (in Russian) [General Theory of Shells and Its Applications in Technology]. Gosudarstvennoe Izdatel’stvo Tehniko-Teoreticeskoi Literatury, Moscow-Leningrad (1949). [Google Scholar]
  34. X. Fu, J. Yong and X. Zhang, Controllability and observability of the heat equation with hyperbolic memory kernel. J. Diff. Equations, 247 (2009), 2395–2439. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.