# Existence and energy decay of a nonuniform Timoshenko system with second sound

Existence and energy decay of a nonuniform Timoshenko system with second sound In this paper, we consider a linear thermoelastic Timoshenko system with variable physical parameters, where the heat conduction is given by Cattaneo’s law and the coupling is via the displacement equation. We discuss the well-posedness and the regularity of solution using the semigroup theory. Moreover, we establish the exponential decay result provided that the stability function $$\chi _{r}(x)=0$$ χ r ( x ) = 0 . Otherwise, we show that the solution decays polynomially. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Zeitschrift für angewandte Mathematik und Physik Springer Journals

# Existence and energy decay of a nonuniform Timoshenko system with second sound

, Volume 69 (1) – Dec 11, 2017
18 pages

/lp/springer_journal/existence-and-energy-decay-of-a-nonuniform-timoshenko-system-with-xm1PfTvnYa
Publisher
Springer International Publishing
Copyright © 2017 by Springer International Publishing AG, part of Springer Nature
Subject
Engineering; Theoretical and Applied Mechanics; Mathematical Methods in Physics
ISSN
0044-2275
eISSN
1420-9039
D.O.I.
10.1007/s00033-017-0897-2
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we consider a linear thermoelastic Timoshenko system with variable physical parameters, where the heat conduction is given by Cattaneo’s law and the coupling is via the displacement equation. We discuss the well-posedness and the regularity of solution using the semigroup theory. Moreover, we establish the exponential decay result provided that the stability function $$\chi _{r}(x)=0$$ χ r ( x ) = 0 . Otherwise, we show that the solution decays polynomially.

### Journal

Zeitschrift für angewandte Mathematik und PhysikSpringer Journals

Published: Dec 11, 2017

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