Gianni Gilardi

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We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a careful development of uniform estimates and the deduction of certain useful boundedness properties, we prove existence(More)
We investigate a nonstandard phase field model of Cahn-Hilliard type. The model, which was introduced in [16], describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in [5], [6] for the case of homogeneous Neumann boundary conditions. In this paper, we investigate the case that(More)
Existence and uniqueness are investigated for a nonlinear diffusion problem of phasefield type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions. This system aims to model two-species phase segregation on an atomic lattice [19]; in the balance equations of(More)
This paper is devoted to the mathematical analysis of a thermomechanical model describing phase transitions in terms of the entropy and order structure balance law. We consider a macroscopic description of the phenomenon and make a presentation of the model. Then, the initial and boundary value problem is addressed for the related PDE system, which contains(More)
This paper is concerned with a diffusion model of phase-field type, consisting of a parabolic system of two partial differential equations, interpreted as balances of microforces and microenergy, for two unknowns: the problem’s order parameter ρ and the chemical potential μ; each equation includes a viscosity term – respectively, ε ∂tμ and δ ∂tρ – with ε(More)
This paper deals with a thermomechanical model describing phase transitions with thermal memory in terms of balance and equilibrium equations for entropy and microforces, respectively. After a presentation and discussion of the model, the large time behaviour of the solutions to the related integro-differential system of PDE’s is investigated.
This paper investigates a nonlocal version of a model for phase separation on an atomic lattice that was introduced by P. Podio-Guidugli in Ric. Mat. 55 (2006) 105-118. The model consists of an initial-boundary value problem for a nonlinearly coupled system of two partial differential equations governing the evolution of an order parameter ρ and the(More)