What is it about?
We study dynamic elastic deformations of plates under the presence of thermal effects ,which are modeledby Cattaneo's Law instead of Fourier 's LawOur main result is the uniform exponential stabilization of the Total Energy for large time.
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Why is it important?
Due to the nonlinearity of the model we study it is almost impossible to obtain analytical expression for the solution.Thus ,in the applications exact properties are always very helpful.
Perspectives
For many years elastic deformations of nonlinear models for plates or shells were treted with thermal effects modeled by heat type equations .This created unconfortable polemic because the parabolic equation gives infinity speed of propagation .Around 60 years ago Cattaneo suggested to consider a perturbation of Fourier's Law which is of Hyperbolic type (which has finite speed of propagation)
Professor Gustavo Alberto Perla Menzala
LNCC
Read the Original
This page is a summary of: Uniform stabilization of a quasilinear plate model in hyperbolic thermoelasticity, Mathematical Methods in the Applied Sciences, December 2015, Wiley,
DOI: 10.1002/mma.3630.
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