Giulio Schimperna

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We discuss a 3D model describing the time evolution of nematic liquid crystals in the framework of Landau-de Gennes theory, where the natural physical constraints are enforced by a singular free energy bulk potential proposed by J.M. Ball and A. Majumdar. The thermal effects are present through the component of the free energy that accounts for(More)
A doubly nonlinear parabolic equation of the form α(u t) − ∆u + W ′ (u) = f , complemented with initial and either Dirichlet or Neumann homogeneous boundary conditions, is addressed. The two nonlinearities are given by the maximal monotone function α and by the derivative W ′ of a smooth but possibly noncon-vex potential W ; f is a known source. After(More)
We consider a diffuse interface model for tumor growth recently proposed in [3]. In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a(More)
2D Cahn-Hilliard equation with inertial term 2 Abstract. P. Galenko et al. proposed a modified Cahn-Hilliard equation to model rapid spinodal decomposition in non-equilibrium phase separation processes. This equation contains an inertial term which causes the loss of any regularizing effect on the solutions. Here we consider an initial and boundary value(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 χ tt , χ being the order parameter, which is linearly coupled with an evolution equation for the (relative)(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)
In this paper we prove the existence of global in time weak solutions for an evolutionary PDE system modelling nonisothermal Landau-de Gennes nematic liquid crystal (LC) flows in three dimensions of space. In our model, the incompressible Navier-Stokes system for the macroscopic velocity u is coupled to a nonlinear convective parabolic equation describing(More)