NDLI: Nonlinear thermoelastic plate equations – Global existence and decay rates for the Cauchy problem

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Nonlinear thermoelastic plate equations – Global existence and decay rates for the Cauchy problem

Content Provider	Semantic Scholar
Author	Racke, Reinhard Ueda, Yoshihiro
Copyright Year	2017
Abstract	Abstract We consider the Cauchy problem in R n for quasilinear thermoelastic Kirchhoff-type plate equations where the heat conduction is modeled by either the Cattaneo law or by the Fourier law. Additionally, we take into account possible inertial effects. Considering nonlinearities which are of fourth-order in the space variable, we deal with a quasilinear system which triggers difficulties typical for nonlinear Schrodinger equations. The different models considered are systems of mixed type comparable to Schrodinger–parabolic or Schrodinger–hyperbolic systems. The main task consists in proving sophisticated a priori estimates leading to obtaining the global existence of solutions for small data, neither known nor expected for the Cauchy problem in pure plate theory nor available before for the coupled system under investigation, where only special cases (bounded domains within with analytic semigroup setting, or the Cauchy problem with semilinear nonlinearities) had been treated before.
Starting Page	8138
Ending Page	8177
Page Count	40
File Format	PDF HTM / HTML
DOI	10.1016/j.jde.2017.08.036
Volume Number	263
Alternate Webpage(s)	https://kops.uni-konstanz.de/bitstream/handle/123456789/38477/Racke_0-403312.pdf?isAllowed=y&sequence=5
Alternate Webpage(s)	http://www.math.uni-konstanz.de/~racke/dvidat/m68.pdf
Alternate Webpage(s)	http://kops.uni-konstanz.de/bitstream/handle/123456789/38477/Racke_0-403312.pdf?isAllowed=y&sequence=5
Alternate Webpage(s)	https://doi.org/10.1016/j.jde.2017.08.036
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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