Maurizio Grasselli

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In the linear theory of elasticity we consider a bounded, compressible, and isotropic body whose mechanical behavior is described by the Lamé system with density and Lamé coefficients depending on the space variables. Assuming null surface displacement on the whole boundary, we first prove an estimate of the surface traction in terms of the energy of the(More)
We consider a differential model describing nonisothermal fast phase separation processes taking place in a three-dimensional bounded domain. This model consists of a viscous Cahn-Hilliard equation characterized by the presence of an inertial term χtt, χ being the order parameter, which is linearly coupled with an evolution equation for the (relative)(More)
In this article, we study the long time behavior of a phase-field parabolichyperbolic system arising from the phase-field theory of phase transitions. This system consists of a parabolic equation governing the (relative) temperature which is nonlinearly coupled with a weakly damped semilinear hyperbolic equation ruling the evolution of the order parameter.(More)
A hyperbolic Stefan problem based on the linearized Gurtin{Pipkin heat conduction law is considered. Temperature and free boundary are controlled by a thermostat acting on the boundary. This feedback control is based on temperature measurements performed by real thermal sensors located into the domain containing the two{phase system and/or at its boundary.(More)
We consider a coupled linear system describing a thermoviscoelastic plate with hereditary effects. The system consists of a hyperbolic integrodifferential equation, governing the temperature, which is linearly coupled with the partial differential equation ruling the evolution of the vertical deflection, presenting a convolution term accounting for memory(More)
We consider a modified Cahn–Hiliard equation where the velocity of the order parameter u depends on the past history of Δμ, μ being the chemical potential with an additional viscous term αut,α 0. This type of equation has been proposed by P. Galenko et al. to model phase separation phenomena in special materials (e.g., glasses). In addition, the usual(More)
The paper is devoted to a modification of the classical Cahn-Hilliard equation proposed by some physicists. This modification is obtained by adding the second time derivative of the order parameter multiplied by an inertial coefficient ε > 0 which is usually small in comparison to the other physical constants. The main feature of this equation is the fact(More)
We consider a diffuse interface model which describes the motion of an incompressible isothermal mixture of two immiscible fluids. This model consists of the Navier-Stokes equations coupled with a convective nonlocal Cahn-Hilliard equation. Several results were already proven by two of the present authors. However, in the two-dimensional case, the(More)
A nonlinear system for the heat diffusion inside a material subject to phase changes is considered. A thermal memory effect is assumed in the heat conduction law; moreover, on account of thermodynamical considerations, a linear growth is allowed for the latent heat density. The resulting problem couples a second order integrodifferential equation, derived(More)