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Existence and exponential decay of solutions to a quasilinear thermoelastic plate system

Lasiecka, Irena; Maad, Sara LU and Sasane, Amol LU (2008) In Nonlinear Differential Equations and Applications 15(6). p.689-715
Abstract
We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain in R^n, n ≤ 3. Existence of finite energy solutions describing the dynamics of a nonlinear thermoelastic plate is established. In addition asymptotic long time behavior of weak solutions is discussed. It is shown that finite energy solutions decay exponentially to zero with the rate depending only on the (finite energy) size of initial conditions. The proofs are based on methods of weak compactness along with nonlocal partial differential operator multipliers which supply the sought after “recovery” inequalities. Regularity of solutions is also discussed by exploiting the underlying analyticity of the linearized... (More)
We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain in R^n, n ≤ 3. Existence of finite energy solutions describing the dynamics of a nonlinear thermoelastic plate is established. In addition asymptotic long time behavior of weak solutions is discussed. It is shown that finite energy solutions decay exponentially to zero with the rate depending only on the (finite energy) size of initial conditions. The proofs are based on methods of weak compactness along with nonlocal partial differential operator multipliers which supply the sought after “recovery” inequalities. Regularity of solutions is also discussed by exploiting the underlying analyticity of the linearized semigroup along with a related maximal parabolic regularity [1, 16, 44]. (Less)
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Quasilinear thermoelastic plates, existence of weak solutions, uniform decays of finite energy solutions
in
Nonlinear Differential Equations and Applications
volume
15
issue
6
pages
27 pages
publisher
Birkhaüser
external identifiers
  • scopus:58149152828
ISSN
1021-9722
DOI
10.1007/s00030-008-0011-8
language
English
LU publication?
no
id
bc922b01-3509-4140-ae9d-8ed684aacd9a
date added to LUP
2017-02-08 13:45:24
date last changed
2017-06-11 05:13:17
@article{bc922b01-3509-4140-ae9d-8ed684aacd9a,
  abstract     = {We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain in R^n, n ≤ 3. Existence of finite energy solutions describing the dynamics of a nonlinear thermoelastic plate is established. In addition asymptotic long time behavior of weak solutions is discussed. It is shown that finite energy solutions decay exponentially to zero with the rate depending only on the (finite energy) size of initial conditions. The proofs are based on methods of weak compactness along with nonlocal partial differential operator multipliers which supply the sought after “recovery” inequalities. Regularity of solutions is also discussed by exploiting the underlying analyticity of the linearized semigroup along with a related maximal parabolic regularity [1, 16, 44].},
  author       = {Lasiecka, Irena and Maad, Sara and Sasane, Amol},
  issn         = {1021-9722},
  keyword      = {Quasilinear thermoelastic plates,existence of weak solutions,uniform decays of finite energy solutions},
  language     = {eng},
  number       = {6},
  pages        = {689--715},
  publisher    = {Birkhaüser},
  series       = {Nonlinear Differential Equations and Applications},
  title        = {Existence and exponential decay of solutions to a quasilinear thermoelastic plate system},
  url          = {http://dx.doi.org/10.1007/s00030-008-0011-8},
  volume       = {15},
  year         = {2008},
}