Advances in Differential Equations

Some properties of shallow shells with thermal effects

F. Travessini De Cezaro and G. Perla Menzala

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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

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

First available in Project Euclid: 4 September 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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