WIAS Preprint No. 2144, (2015)

Generalized gradient flow structure of internal energy driven phase field systems



Authors

  • Bonetti, Elena
  • Rocca, Elisabetta

2010 Mathematics Subject Classification

  • 74N25 82B26 35A01 35A02

Keywords

  • gradient flow, phase field systems, existence of weak solutions, uniqueness

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.

Appeared in

  • ESAIM Control Optim. Calc. Var. 23 (2017) pp. 1201--1216, changed title: Unified gradient flow structure of phase field systems via a generalized principle of virtual powers.

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