### 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