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Generalized gradient flow structure of internal energy driven phase field systems

Authors
  • Bonetti, Elena
  • Rocca, Elisabetta
Type
Preprint
Publication Date
Jul 14, 2015
Submission Date
Jul 14, 2015
Identifiers
arXiv ID: 1507.03818
Source
arXiv
License
Yellow
External links

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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