Luca Bisconti

Harmonic perturbations with delay of periodic separated variables differential equations

We study the structure of the set of harmonic solutions to perturbed, nonautonomous,

Existence Results in The Linear Dynamics of Quasicrystals with Phason Diffusion and Nonlinear Gyroscopic Effects

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About the notion of non‐T‐resonance and applications to topological multiplicity results for ODEs on differentiable manifolds

-periodic, separated variables ODEs on manifolds. The perturbing term, supposed to be

A model of isotropic damage with strain-gradient effects: existence and uniqueness of weak solutions for progressive damage processes

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On the existence of an inertial manifold for a deconvolution model of the 2D mean Boussinesq equations

-periodic in time, is allowed to contain a finite delay. Our main result extends those of \cite{FS09} and \cite{spaSepVar} but it cannot be simply deduced from them: It emerges from of a combination of the techniques exposed in those two papers.

On the convergence of an approximate deconvolution model to the 3D mean Boussinesq equations

Quasicrystals are characterized by quasi-periodic arrangements of atoms. The description of their mechanics involves deformation and a (so called phason) vector field accounting at macroscopic scale of local phase changes, due to atomic flips necessary to match quasi-periodicity under the action of the external environment. Here we discuss the mechanics of quasicrystals, commenting the shift from its initial formulation, as standard elasticity in a space with dimension twice the ambient one, to a more elaborated setting avoiding physical inconveniences of the original proposal. In the new setting we tackle two problems. First we discuss the linear dynamics of quasicrystals including a phason diffusion. We prove existence of weak solutions and their uniqueness under rather general boundary and initial conditions. We then consider phason rotational inertia, non-linearly coupled with the curl of the macroscopic velocity, and prove once again existence of weak solutions to the pertinent balance equations.

On a class of differential-algebraic equations with infinite delay

By using topological methods, mainly the degree of a tangent vector field, we establish multiplicity results for

CORRIGENDUM TO ON A CLASS OF DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH INFINITE DELAY

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Global well-posedness of the two-dimensional horizontally filtered simplified Bardina turbulence model on a strip-like region

-periodic solutions of parametrized

Sunflower model: time-dependent coefficients and topology of the periodic solutions set

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