Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010Spectral problems. Issue dedicated to the memory of M. Birman
|Page(s)||4 - 31|
|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.
- 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.
- S. A. Avdonin and B. P. Belinskiy, On controllability of a rotating string. J. Math. Anal. Appl., 321 (2006), 198–212. [CrossRef] [MathSciNet]
- 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]
- 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.
- S. A. Avdonin and S. A. Ivanov, Exponential Riesz bases of subspaces and divided differences. St. Petersburg Mathematical Journal, 13 (2001), 339–351.
- 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.
- S. Avdonin and W. Moran, Ingham type inequalities and Riesz bases of divided differences. Int. J. Appl. Math. Comput. Sci., 11 (2001), 101–118.
- 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]
- 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]
- V. Barbu and M. Iannelli, Approximate controllability of the heat equation with memory. Differential and Integral Equations, 13 (2000), 1393–1412. [MathSciNet]
- 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]
- 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.
- A. Erdélyi. Asymptotic Expansions. Dover Publications, Inc., 1956.
- 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.
- J. P. Den Hartog. Mechanical Vibrations. McGraw-Hill Book Company, New York, 1956.
- 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]
- T. von Kàrmàn and M. A. Biot. Mathematical Methods in Engineering. McGraw-Hill Book Company, New York, 1940.
- O. A. Ladyzhenskaia. The Boundary Value Problems of Mathematical Physics. Springer-Verlag, New York, 1985.
- 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.
- N. W. McLachlan. Theory and Applications of Mathieu Functions, Oxford, 1947.
- 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]
- L. Pandolfi, The controllability of the Gurtin-Pipkin equation: a cosine operator approach. Applied Mathematics and Optimization, 52 (2005), 143–165. [CrossRef] [MathSciNet]
- L. Pandolfi, Riesz system and the controllability of heat equations with memory. Integral Eq. Oper. Theory, 64 (2009), 429–453. [CrossRef]
- 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).
- 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).
- D. L. Russell, Nonharmonic Fourier series in the control theory of distributed parameter systems. J. Math. Anal. Appl., 18 (1967), 542–559. [CrossRef] [MathSciNet]
- D. L. Russell, Controllability and stabilizability theory for linear partial differential equations. SIAM Review, 20 (1978), 639–739. [CrossRef] [MathSciNet]
- D. L. Russell, On exponential bases for the Sobolev spaces over an interval. J. Math.Anal.Appl., 87 (1982), 528–550. [CrossRef] [MathSciNet]
- W. Soedel. Vibrations of Shells and Plates. Marcel Dekker, Inc., New York, 1993.
- M. E. Taylor. Pseudodifferential Operators. Princeton University Press, Princeton, NJ, 1981.
- S. Timoshenko. Thèorie des Vibrations. Libr. Polytecnique Ch Bèranger, Paris, 1947.
- 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).
- 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]
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.