Backward Uniqueness in Linear Thermoelasticity with Time and Space Variable Coefficients

  • Herbert Koch
  • Irena Lasiecka


Backward uniqueness for thermoelastic plates and thermoelastic waves with time- and space-dependent coefficients is established. While this result has been proved recently, in the case of time-independent coefficients, it is new for the case of time-dependent coefficients. The proof relies on a combination of energy and Carleman’s estimates, hence it is very different from the one given in [LRT], which is based on complex analysis methods. These latter methods are not applicable to nonlinear models and to models with time-dependent coefficients. Our results have consequences for several nonlinear models of thermoelasticity.


Energy Estimate Lumer Volume Homogeneous Dirichlet Boundary Condition Carleman Estimate Plate Equation 
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  1. [G]
    P. Grisvard, Elliptic Problems in Non-Smooth Domains, Pittman, Boston, 1985.Google Scholar
  2. [I]
    V. Isakov, On the uniqueness of continuation for a thermoelasticity system. SIAM J. Math. Analysis, 33 (2001), 509–522.MATHCrossRefMathSciNetGoogle Scholar
  3. [LRT]
    I. Lasiecka, M. Renardy, and R. Triggiani, Backward uniqueness of thermoelastic plates with rotational forces, Semigroup Forum, 62 (2001), 217–242.MATHMathSciNetGoogle Scholar
  4. [LL]
    J. Lagnese and J.L. Lions, Modeling, Analysis and Control of Thin Plates, Masson, 1988.Google Scholar
  5. [L1]
    J. Lagnese, Boundary Stabilization of Thin Plates, SIAM, Philadelphia, 1989.MATHGoogle Scholar
  6. [L2]
    J. Lagnese, The reachability problem for thermoelastic plates, Arch Rational Mechanics and Analysis 112 (1990), 223–267.MATHCrossRefMathSciNetGoogle Scholar
  7. [LR]
    Z. Liu and M. Renardy, A note on the equation of thermoelastic plate, Applied Math. Letters, 8 (1995), 1–6.CrossRefMathSciNetGoogle Scholar
  8. [LT]
    I. Lasiecka and R. Triggiani, Analyticity of thermo-elastic semigroups with free B.C., Annali di Scuola Normale Superiore, XXVII (1998), 457–482.MathSciNetGoogle Scholar
  9. [LT1]
    I. Lasiecka and R. Triggiani, Control Theory for Partial Differential Equations, Cambridge University Press, 2001.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Herbert Koch
    • 1
  • Irena Lasiecka
    • 2
  1. 1.Mathematisches InstitutUniversität BonnBonnGermany
  2. 2.Department of MathematicsCharlottesvilleUSA

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