November  2010, 14(4): 1487-1510. doi: 10.3934/dcdsb.2010.14.1487

Riesz systems and moment method in the study of viscoelasticity in one space dimension

1. 

Politecnico di Torino, Dipartimento di Matematica, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Received  June 2009 Revised  January 2010 Published  August 2010

In this paper we study the equation of linear viscoelasticity and we prove that two sequences of functions, naturally associated with this equation, are Riesz systems. These sequences appear naturally when observability and controllability problems are reformulated in terms of suitable interpolation/moment problems.
   The key contribution of the paper is to be found in the way used to prove that the two sequences are Riesz systems, an idea already applied to the study of different control problems.
Citation: Luciano Pandolfi. Riesz systems and moment method in the study of viscoelasticity in one space dimension. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1487-1510. doi: 10.3934/dcdsb.2010.14.1487
[1]

Lingyang Liu, Xu Liu. Controllability and observability of some coupled stochastic parabolic systems. Mathematical Control and Related Fields, 2018, 8 (3&4) : 829-854. doi: 10.3934/mcrf.2018037

[2]

Zhaoqiang Ge. Controllability and observability of stochastic implicit systems and stochastic GE-evolution operator. Numerical Algebra, Control and Optimization, 2022, 12 (2) : 339-351. doi: 10.3934/naco.2021009

[3]

Tatsien Li, Bopeng Rao, Zhiqiang Wang. Exact boundary controllability and observability for first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 243-257. doi: 10.3934/dcds.2010.28.243

[4]

Rafał Kamocki, Marek Majewski. On the continuous dependence of solutions to a fractional Dirichlet problem. The case of saddle points. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2557-2568. doi: 10.3934/dcdsb.2014.19.2557

[5]

Chun Zong, Gen Qi Xu. Observability and controllability analysis of blood flow network. Mathematical Control and Related Fields, 2014, 4 (4) : 521-554. doi: 10.3934/mcrf.2014.4.521

[6]

Abdelmouhcene Sengouga. Exact boundary observability and controllability of the wave equation in an interval with two moving endpoints. Evolution Equations and Control Theory, 2020, 9 (1) : 1-25. doi: 10.3934/eect.2020014

[7]

Ali Wehbe, Marwa Koumaiha, Layla Toufaily. Boundary observability and exact controllability of strongly coupled wave equations. Discrete and Continuous Dynamical Systems - S, 2022, 15 (5) : 1269-1305. doi: 10.3934/dcdss.2021091

[8]

Gabriella Pinzari. Global Kolmogorov tori in the planetary $\boldsymbol N$-body problem. Announcement of result. Electronic Research Announcements, 2015, 22: 55-75. doi: 10.3934/era.2015.22.55

[9]

Nicolas Augier, Ugo Boscain, Mario Sigalotti. Semi-conical eigenvalue intersections and the ensemble controllability problem for quantum systems. Mathematical Control and Related Fields, 2020, 10 (4) : 877-911. doi: 10.3934/mcrf.2020023

[10]

Luciano Pandolfi. Riesz systems, spectral controllability and a source identification problem for heat equations with memory. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 745-759. doi: 10.3934/dcdss.2011.4.745

[11]

Paola Loreti, Daniela Sforza. Observability of $N$-dimensional integro-differential systems. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 745-757. doi: 10.3934/dcdss.2016026

[12]

Florian Méhats, Olivier Pinaud. A problem of moment realizability in quantum statistical physics. Kinetic and Related Models, 2011, 4 (4) : 1143-1158. doi: 10.3934/krm.2011.4.1143

[13]

Peter Bella, Arianna Giunti. Green's function for elliptic systems: Moment bounds. Networks and Heterogeneous Media, 2018, 13 (1) : 155-176. doi: 10.3934/nhm.2018007

[14]

Orazio Arena. A problem of boundary controllability for a plate. Evolution Equations and Control Theory, 2013, 2 (4) : 557-562. doi: 10.3934/eect.2013.2.557

[15]

Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3837-3849. doi: 10.3934/dcdss.2020444

[16]

John E. Lagnese. Controllability of systems of interconnected membranes. Discrete and Continuous Dynamical Systems, 1995, 1 (1) : 17-33. doi: 10.3934/dcds.1995.1.17

[17]

Yassine El Gantouh, Said Hadd, Abdelaziz Rhandi. Approximate controllability of network systems. Evolution Equations and Control Theory, 2021, 10 (4) : 749-766. doi: 10.3934/eect.2020091

[18]

Lianwen Wang. Approximate controllability and approximate null controllability of semilinear systems. Communications on Pure and Applied Analysis, 2006, 5 (4) : 953-962. doi: 10.3934/cpaa.2006.5.953

[19]

Belkacem Said-Houari, Salim A. Messaoudi. General decay estimates for a Cauchy viscoelastic wave problem. Communications on Pure and Applied Analysis, 2014, 13 (4) : 1541-1551. doi: 10.3934/cpaa.2014.13.1541

[20]

Yinnian He, Yi Li. Asymptotic behavior of linearized viscoelastic flow problem. Discrete and Continuous Dynamical Systems - B, 2008, 10 (4) : 843-856. doi: 10.3934/dcdsb.2008.10.843

2020 Impact Factor: 1.327

Metrics

  • PDF downloads (52)
  • HTML views (0)
  • Cited by (17)

Other articles
by authors

[Back to Top]