American Institute of Mathematical Sciences

Advanced
July  1999, 5(3): 585-598. doi: 10.3934/dcds.1999.5.585

A sharp trace result on a thermo-elastic plate equation with coupled hinged/Neumann boundary conditions

Irena Lasiecka 1, and  Roberto Triggiani 2,

1. 

Department of Mathematics, University of Virginia, Charlottesville, VA 22903
2. 

Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904

Received  November 1998 Revised  February 1998 Published  May 1999

We consider a thermo-elastic plate equation with rotational forces [Lagnese.1] and with coupled hinged mechanical/Neumann thermal boundary conditions (B.C.). We give a sharp result on the Neumann trace of the mechanical velocity, which is "$\frac{1}{2}$" sharper in the space variable than the result than one would obtain by a formal application of trace theory on the optimal interior regularity. Two proofs by energy methods are given: one which reduces the analysis to sharp wave equation's regularity theory; and one which analyzes directly the corresponding Kirchoff elastic equation. Important implications of this result are noted.
Keywords: hinged/Neumann boundary conditions, sharp trace regularity., Thermo-elastic plate equations.
Mathematics Subject Classification: 35 .
Citation: Irena Lasiecka, Roberto Triggiani. A sharp trace result on a thermo-elastic plate equation with coupled hinged/Neumann boundary conditions. Discrete & Continuous Dynamical Systems, 1999, 5 (3) : 585-598. doi: 10.3934/dcds.1999.5.585
[1]

Roberto Triggiani. Sharp regularity theory of second order hyperbolic equations with Neumann boundary control non-smooth in space. Evolution Equations & Control Theory, 2016, 5 (4) : 489-514. doi: 10.3934/eect.2016016
[2]

Katerina Nik. On a free boundary model for three-dimensional MEMS with a hinged top plate II: Parabolic case. Communications on Pure & Applied Analysis, 2021, 20 (10) : 3379-3401. doi: 10.3934/cpaa.2021110
[3]

Zhenhua Zhang. Asymptotic behavior of solutions to the phase-field equations with neumann boundary conditions. Communications on Pure & Applied Analysis, 2005, 4 (3) : 683-693. doi: 10.3934/cpaa.2005.4.683
[4]

Shu Luan. On the existence of optimal control for semilinear elliptic equations with nonlinear neumann boundary conditions. Mathematical Control & Related Fields, 2017, 7 (3) : 493-506. doi: 10.3934/mcrf.2017018
[5]

Jason Metcalfe, Jacob Perry. Global solutions to quasilinear wave equations in homogeneous waveguides with Neumann boundary conditions. Communications on Pure & Applied Analysis, 2012, 11 (2) : 547-556. doi: 10.3934/cpaa.2012.11.547
[6]

Minoo Kamrani. Numerical solution of partial differential equations with stochastic Neumann boundary conditions. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5337-5354. doi: 10.3934/dcdsb.2019061
[7]

Giovanni Cupini, Paolo Marcellini, Elvira Mascolo. Regularity under sharp anisotropic general growth conditions. Discrete & Continuous Dynamical Systems - B, 2009, 11 (1) : 67-86. doi: 10.3934/dcdsb.2009.11.67
[8]

Alberto Ferrero, Filippo Gazzola. A partially hinged rectangular plate as a model for suspension bridges. Discrete & Continuous Dynamical Systems, 2015, 35 (12) : 5879-5908. doi: 10.3934/dcds.2015.35.5879
[9]

Antonino Morassi, Edi Rosset, Sergio Vessella. Unique determination of a cavity in an elastic plate by two boundary measurements. Inverse Problems & Imaging, 2007, 1 (3) : 481-506. doi: 10.3934/ipi.2007.1.481
[10]

T. J. Christiansen. Resonances and balls in obstacle scattering with Neumann boundary conditions. Inverse Problems & Imaging, 2008, 2 (3) : 335-340. doi: 10.3934/ipi.2008.2.335
[11]

Eugenio Montefusco, Benedetta Pellacci, Gianmaria Verzini. Fractional diffusion with Neumann boundary conditions: The logistic equation. Discrete & Continuous Dynamical Systems - B, 2013, 18 (8) : 2175-2202. doi: 10.3934/dcdsb.2013.18.2175
[12]

Mariane Bourgoing. Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions. Discrete & Continuous Dynamical Systems, 2008, 21 (3) : 763-800. doi: 10.3934/dcds.2008.21.763
[13]

Michela Eleuteri, Jana Kopfová, Pavel Krejčí. Fatigue accumulation in a thermo-visco-elastoplastic plate. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2091-2109. doi: 10.3934/dcdsb.2014.19.2091
[14]

Andrzej Nowakowski. Variational analysis of semilinear plate equation with free boundary conditions. Discrete & Continuous Dynamical Systems, 2015, 35 (7) : 3133-3154. doi: 10.3934/dcds.2015.35.3133
[15]

Robert Denk, Yoshihiro Shibata. Generation of semigroups for the thermoelastic plate equation with free boundary conditions. Evolution Equations & Control Theory, 2019, 8 (2) : 301-313. doi: 10.3934/eect.2019016
[16]

Scott W. Hansen, Oleg Yu Imanuvilov. Exact controllability of a multilayer Rao-Nakra plate with free boundary conditions. Mathematical Control & Related Fields, 2011, 1 (2) : 189-230. doi: 10.3934/mcrf.2011.1.189
[17]

Mengni Li. Global regularity for a class of Monge-Ampère type equations with nonzero boundary conditions. Communications on Pure & Applied Analysis, 2021, 20 (1) : 301-317. doi: 10.3934/cpaa.2020267
[18]

Peter Weidemaier. Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed $L_p$-norm. Electronic Research Announcements, 2002, 8: 47-51.

[19]

Shitao Liu, Roberto Triggiani. Recovering damping and potential coefficients for an inverse non-homogeneous second-order hyperbolic problem via a localized Neumann boundary trace. Discrete & Continuous Dynamical Systems, 2013, 33 (11&12) : 5217-5252. doi: 10.3934/dcds.2013.33.5217
[20]

David L. Russell. Trace properties of certain damped linear elastic systems. Evolution Equations & Control Theory, 2013, 2 (4) : 711-721. doi: 10.3934/eect.2013.2.711

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (48)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences