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, possibly including the thermal one. In particular, through a suitable choice of the driving functional, we formally get a gradient flow 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 mechanical ones). We prove a global in time existence of (a suitably defined 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.

Accepted:

DOI: 10.1051/cocv/2016051

Keywords: Gradient flow, phase field systems, existence of weak solutions, uniqueness

^{1}; Rocca, Elisabetta

^{2}

@article{COCV_2017__23_3_1201_0, author = {Bonetti, Elena and Rocca, Elisabetta}, title = {Unified gradient flow structure of phase field systems via a generalized principle of virtual powers}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1201--1216}, publisher = {EDP-Sciences}, volume = {23}, number = {3}, year = {2017}, doi = {10.1051/cocv/2016051}, zbl = {1365.74140}, mrnumber = {3660465}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2016051/} }

TY - JOUR AU - Bonetti, Elena AU - Rocca, Elisabetta TI - Unified gradient flow structure of phase field systems via a generalized principle of virtual powers JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1201 EP - 1216 VL - 23 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016051/ DO - 10.1051/cocv/2016051 LA - en ID - COCV_2017__23_3_1201_0 ER -

%0 Journal Article %A Bonetti, Elena %A Rocca, Elisabetta %T Unified gradient flow structure of phase field systems via a generalized principle of virtual powers %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1201-1216 %V 23 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016051/ %R 10.1051/cocv/2016051 %G en %F COCV_2017__23_3_1201_0

Bonetti, Elena; Rocca, Elisabetta. Unified gradient flow structure of phase field systems via a generalized principle of virtual powers. ESAIM: Control, Optimisation and Calculus of Variations, Volume 23 (2017) no. 3, pp. 1201-1216. doi : 10.1051/cocv/2016051. http://archive.numdam.org/articles/10.1051/cocv/2016051/

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