Unified gradient flow structure of phase field systems via a generalized principle of virtual powers
Articolo
Data di Pubblicazione:
2017
Citazione:
Unified gradient flow structure of phase field systems via a generalized principle of virtual powers / E. Bonetti, E. Rocca. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - 23(2017), pp. 1201-1216.
Abstract:
In this paper we introduce a general abstract formulation of a variational
thermomechanical model by means of a unied derivation via a generalization
of the principle of virtual powers for all the variables of the system, possibly
including the thermal one. In particular, through a suitable choice of the driv-
ing functional, we formally get a gradient
ow structure (in a suitable abstract
setting) for the whole nonlinear PDE system. In this framework, the equations
may be interpreted as internal balance equations of forces (e.g., thermal or me-
chanical ones). We prove a global in time existence of (a suitably dened weak)
solutions for the Cauchy problem associated to the abstract PDE system as well
as uniqueness in case of suitable smoothness assumptions on the functionals.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
gradient fow, phase field systems, existence of weak solutions, uniqueness
Elenco autori:
E. Bonetti, E. Rocca
Link alla scheda completa: