## Advances in Differential Equations

### Some properties of shallow shells with thermal effects

#### Abstract

We consider a dynamical nonlinear model for shallow shells of the Marguerre--Vlasov's type in the presence of thermal effects. Results on existence and uniqueness of global weak solutions are already available. We consider the above model depending on a parameter $\varepsilon>0$ and study its weak limit as $\varepsilon\rightarrow 0^+$. The limit model turns out to be a nonlinear Timoshenko's equation with thermal effects on the manifold (the shell). We also analyze the asymptotic behavior of the total energy of the nonlinear model of Marguerre--Vlasov's type with thermal effects.

#### Article information

Source
Adv. Differential Equations Volume 18, Number 11/12 (2013), 1073-1104.

Dates
First available in Project Euclid: 4 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1378327379

Mathematical Reviews number (MathSciNet)
MR3129018

Zentralblatt MATH identifier
1309.35166

Subjects
Primary: 58G20 58Z05: Applications to physics 35Q72 74K25: Shells

#### Citation

Menzala, G. Perla; De Cezaro, F. Travessini. Some properties of shallow shells with thermal effects. Adv. Differential Equations 18 (2013), no. 11/12, 1073--1104.https://projecteuclid.org/euclid.ade/1378327379