arXiv subjects

Maria Grazia Naso

Publications and source records attributed to Maria Grazia Naso.

4 recordsLinked to original sources

arXiv2026

Unified structures for solutions of Painlevé equation II and Somos-4 like relations for the tau functions

We present certain general structures related to the solutions of Painlevé equation II and to the solutions of the differential equation satisfied by the corresponding Hamiltonian equations, together with the tau functions. By taking advantage of the Bäcklund transformations we find different explicit rational expressions linking the solutions of Painlevé equation II, Painlevé equation XXXIV and the Hamiltonians with the tau functions. Wronskians among different tau functions and the derivatives of the tau functions themselves will be expressed in terms of rational functions of tau functions too. A non-autonomous Somos-4 type relation solved by these functions is given. For the Somos-4 type relation we consider degenerate cases through the use of suitable parameters inserted into the equations: the autonomous case solvable in terms of Weierstrass elliptic functions, the case corresponding to the Yablonskii-Vorob'ev polynomials, the Airy-type solutions and the more general transcendental case.

nlin.SI↗

arXiv2025

Global attractors for the Signorini problem with pointwise damping

The existence of global attractors is investigated for the Signorini problem with pointwise dissipation. It is shown that both the semilinear Signorini problem and the elastic obstacle problem with normal compliance exhibit exponential decay to zero and admit compact global attractors. To establish these results, the original problem is approximated by a hybrid PDE-ODE system, which allows for a rigorous analysis of well-posedness and the long-time behavior of its solutions.

math.AP↗

arXiv2025

The Gevrey class of the Euler-Bernoulli beam model with singularities

We study the Euler-Bernoulli beam model with singularities at the points $x=ξ_1$, $x=ξ_2$ and with localized viscoelastic dissipation of Kelvin-Voigt type. We assume that the beam is composed by two materials; one is an elastic material and the other one is a viscoelastic material of Kelvin-Voigt type. Our main result is that the corresponding semigroup is immediately differentiable and also of Gevrey class $4$. In particular, our result implies that the model is exponentially stable, has the linear stability property, and the smoothing effect property over the initial data.

math.AP↗

arXiv2020

Non rectification of heat in graded Si-Ge alloys

We investigate the possibility to obtain a thermal diode with functionally graded Si-Ge alloys. A wire with variable section is considered. After the introduction of a formula giving the thermal conductivity of the wire as a function of the species content and of the diameter of the wire, numerical and analytical results are presented supporting the impracticability to get a thermal diode with the characteristics here considered. However, the present study opens the way to further generalisations amenable to give applicative promising results.

cond-mat.other↗