Existence and exponential decay of solutions to a quasilinear thermoelastic plate system
(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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https://lup.lub.lu.se/record/bc922b01-3509-4140-ae9d-8ed684aacd9a
- author
- Lasiecka, Irena ; Maad, Sara LU and Sasane, Amol LU
- publishing date
- 2008
- 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
- Birkhäuser Verlag
- 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
- 2022-01-30 17:48:31
@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}},
keywords = {{Quasilinear thermoelastic plates; existence of weak solutions; uniform decays of finite energy solutions}},
language = {{eng}},
number = {{6}},
pages = {{689--715}},
publisher = {{Birkhäuser Verlag}},
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}},
doi = {{10.1007/s00030-008-0011-8}},
volume = {{15}},
year = {{2008}},
}