
Previous Article
Homoclinic orbits in a disease transmission model with nonlinear incidence and nonconstant population
 DCDSB Home
 This Issue

Next Article
Chaotic advection, transport and patchiness in clouds of pollution in an estuarine flow
The coupled PDE system of a composite (sandwich) beam revisited
1.  Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904 
In addition, however, through the aforementioned reduction to thermoelastic problems, we here establish new results for sandwich beams, when rotational forces are accounted for. They include: (i) a backward uniqueness property (Section 4), and (ii) a suitable singular estimate, critical in control theory (Section 5). Finally, we obtain a new backward uniqueness property, this time for a structural acoustic chamber having a composite (sandwich) beam as its flexible wall (Section 6).
[1] 
Kokum R. De Silva, Tuoc V. Phan, Suzanne Lenhart. Advection control in parabolic PDE systems for competitive populations. Discrete & Continuous Dynamical Systems  B, 2017, 22 (3) : 10491072. doi: 10.3934/dcdsb.2017052 
[2] 
Martin Schechter. Monotonicity methods for infinite dimensional sandwich systems. Discrete & Continuous Dynamical Systems  A, 2010, 28 (2) : 455468. doi: 10.3934/dcds.2010.28.455 
[3] 
David L. Russell. Modeling and control of hybrid beam systems with rotating tip component. Evolution Equations & Control Theory, 2014, 3 (2) : 305329. doi: 10.3934/eect.2014.3.305 
[4] 
Roberto Triggiani. Sharp regularity of hyperbolicdominated thermoelastic systems with point control: the clamped case. Conference Publications, 2007, 2007 (Special) : 9931004. doi: 10.3934/proc.2007.2007.993 
[5] 
Enrique FernándezCara, Diego A. Souza. On the control of some coupled systems of the Boussinesq kind with few controls. Mathematical Control & Related Fields, 2012, 2 (2) : 121140. doi: 10.3934/mcrf.2012.2.121 
[6] 
Wenmin Gong, Guangcun Lu. On coupled Dirac systems. Discrete & Continuous Dynamical Systems  A, 2017, 37 (8) : 43294346. doi: 10.3934/dcds.2017185 
[7] 
Reinhard Racke. Instability of coupled systems with delay. Communications on Pure & Applied Analysis, 2012, 11 (5) : 17531773. doi: 10.3934/cpaa.2012.11.1753 
[8] 
R.H. Fabiano, Scott W. Hansen. Modeling and analysis of a threelayer damped sandwich beam. Conference Publications, 2001, 2001 (Special) : 143155. doi: 10.3934/proc.2001.2001.143 
[9] 
Aaron A. Allen, Scott W. Hansen. Analyticity and optimal damping for a multilayer MeadMarkus sandwich beam. Discrete & Continuous Dynamical Systems  B, 2010, 14 (4) : 12791292. doi: 10.3934/dcdsb.2010.14.1279 
[10] 
A. Özkan Özer, Scott W. Hansen. Uniform stabilization of a multilayer RaoNakra sandwich beam. Evolution Equations & Control Theory, 2013, 2 (4) : 695710. doi: 10.3934/eect.2013.2.695 
[11] 
Scott W. Hansen, Rajeev Rajaram. Riesz basis property and related results for a RaoNakra sandwich beam. Conference Publications, 2005, 2005 (Special) : 365375. doi: 10.3934/proc.2005.2005.365 
[12] 
Rajeev Rajaram, Scott W. Hansen. Null controllability of a damped MeadMarkus sandwich beam. Conference Publications, 2005, 2005 (Special) : 746755. doi: 10.3934/proc.2005.2005.746 
[13] 
Salim A. Messaoudi, Abdelfeteh Fareh. Exponential decay for linear damped porous thermoelastic systems with second sound. Discrete & Continuous Dynamical Systems  B, 2015, 20 (2) : 599612. doi: 10.3934/dcdsb.2015.20.599 
[14] 
Flank D. M. Bezerra, Vera L. Carbone, Marcelo J. D. Nascimento, Karina Schiabel. Pullback attractors for a class of nonautonomous thermoelastic plate systems. Discrete & Continuous Dynamical Systems  B, 2018, 23 (9) : 35533571. doi: 10.3934/dcdsb.2017214 
[15] 
R. Demarque, J. Límaco, L. Viana. Local null controllability of coupled degenerate systems with nonlocal terms and one control force. Evolution Equations & Control Theory, 2019, 0 (0) : 00. doi: 10.3934/eect.2020026 
[16] 
Matthias Gerdts, SvenJoachim Kimmerle. Numerical optimal control of a coupled ODEPDE model of a truck with a fluid basin. Conference Publications, 2015, 2015 (special) : 515524. doi: 10.3934/proc.2015.0515 
[17] 
Andrew D. Lewis. Linearisation of tautological control systems. Journal of Geometric Mechanics, 2016, 8 (1) : 99138. doi: 10.3934/jgm.2016.8.99 
[18] 
Fatiha AlabauBoussouira. On the influence of the coupling on the dynamics of singleobserved cascade systems of PDE's. Mathematical Control & Related Fields, 2015, 5 (1) : 130. doi: 10.3934/mcrf.2015.5.1 
[19] 
Wenxiong Chen, Congming Li. Super polyharmonic property of solutions for PDE systems and its applications. Communications on Pure & Applied Analysis, 2013, 12 (6) : 24972514. doi: 10.3934/cpaa.2013.12.2497 
[20] 
Felipe Wallison ChavesSilva, Sergio Guerrero, Jean Pierre Puel. Controllability of fast diffusion coupled parabolic systems. Mathematical Control & Related Fields, 2014, 4 (4) : 465479. doi: 10.3934/mcrf.2014.4.465 
2018 Impact Factor: 1.008
Tools
Metrics
Other articles
by authors
[Back to Top]