Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010
Spectral problems. Issue dedicated to the memory of M. Birman
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Page(s) | 4 - 31 | |
DOI | https://doi.org/10.1051/mmnp/20105401 | |
Published online | 12 May 2010 |
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- S. A. Avdonin and W. Moran, Simultaneous control problems for systems of elastic strings and beams. Systems and Control Letters, 44 (2001), 147–155. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- V. Barbu and M. Iannelli, Approximate controllability of the heat equation with memory. Differential and Integral Equations, 13 (2000), 1393–1412. [MathSciNet] [Google Scholar]
- 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]
- 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]
- A. Erdélyi. Asymptotic Expansions. Dover Publications, Inc., 1956. [Google Scholar]
- 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]
- J. P. Den Hartog. Mechanical Vibrations. McGraw-Hill Book Company, New York, 1956. [Google Scholar]
- 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]
- T. von Kàrmàn and M. A. Biot. Mathematical Methods in Engineering. McGraw-Hill Book Company, New York, 1940. [Google Scholar]
- O. A. Ladyzhenskaia. The Boundary Value Problems of Mathematical Physics. Springer-Verlag, New York, 1985. [Google Scholar]
- 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]
- N. W. McLachlan. Theory and Applications of Mathieu Functions, Oxford, 1947. [Google Scholar]
- 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]
- L. Pandolfi, The controllability of the Gurtin-Pipkin equation: a cosine operator approach. Applied Mathematics and Optimization, 52 (2005), 143–165. [Google Scholar]
- L. Pandolfi, Riesz system and the controllability of heat equations with memory. Integral Eq. Oper. Theory, 64 (2009), 429–453. [Google Scholar]
- 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]
- 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]
- 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]
- D. L. Russell, Controllability and stabilizability theory for linear partial differential equations. SIAM Review, 20 (1978), 639–739. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- W. Soedel. Vibrations of Shells and Plates. Marcel Dekker, Inc., New York, 1993. [Google Scholar]
- M. E. Taylor. Pseudodifferential Operators. Princeton University Press, Princeton, NJ, 1981. [Google Scholar]
- S. Timoshenko. Thèorie des Vibrations. Libr. Polytecnique Ch Bèranger, Paris, 1947. [Google Scholar]
- 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]
- 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]
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