Calculus of Variations and Geometric Measure Theory
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E. Bonetti - E. Rocca

Generalized gradient flow structure of internal energy driven phase field systems

created by rocca on 15 Oct 2015
modified on 16 Oct 2015

[BibTeX]

Preprint

Inserted: 15 oct 2015
Last Updated: 16 oct 2015

Year: 2015

Abstract:

In this paper we introduce a general abstract formulation of a variational thermomechanical model, by means of a unified derivation via a generalization of the principle of virtual powers for all the variables of the system, including the thermal one. In particular, choosing as thermal variable the entropy of the system, and as driving functional the internal energy, we get a gradient flow structure (in a suitable abstract setting) for the whole nonlinear PDE system. We prove a global in time existence of (weak) solutions result for the Cauchy problem associated to the abstract PDE system as well as uniqueness in case of suitable smoothness assumptions on the functionals.

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