arXiv subjects

Carmen Perugia

Publications and source records attributed to Carmen Perugia.

5 recordsLinked to original sources

arXiv2025

Effective thermal conduction of a Signorini-type problem in composites with rough interface

We analyse the effect of a Signorini-type interface condition on the asymptotic behaviour, as ε tends to zero, of a problem posed in an open bounded cylinder of {R^N}, {N\geq 2}, divided in two connected components by an imperfect rough surface. The Signorini-type condition is expressed by means of two complementary equalities involving the jump of the solution on the interface and its conormal derivative via a parameter γ. Different limit problems are obtained according to the values of γ and the amplitude of the interface oscillations.

math.AP↗

arXiv2024

On the homogenization of a Signorini-type problem in a domain with inclusions

In this paper we investigate the effect of a Signorini-type interface condition on the asymptotic behaviour, as $\varepsilon$ tends to zero, of problems posed in $\varepsilon$-periodic domains with inclusions. The Signorini-type condition is expressed in terms of two complementary equalities involving the jump of the solution on the interface and its conormal derivative via a parameter $γ$. Our problem models the heat exchange in a medium hosting an $\varepsilon$-periodic array of thermal conductors in presence of impurities distributed on some regions of the interface. Different limit problems are obtained according to different values of $γ$.

math.AP↗

arXiv2020

A Ginzburg-Landau type energy with weight and with convex potential near zero

In this paper, we study the asymptotic behaviour of minimizing solutions of a Ginzburg-Landau type functional with a positive weight and with convex potential near $0$ and we estimate the energy in this case. We also generalize a lower bound for the energy of unit vector field given initially by Brezis-Merle-Rivière.

math.AP↗

arXiv2020

Asymptotic behavior of a Bingham Flow in thin domains with rough boundary

We consider an incompressible Bingham flow in a thin domain with rough boundary, under the action of given external forces and with no-slip boundary condition on the whole boundary of the domain. In mathematical terms, this problem is described by non linear variational inequalities over domains where a small parameter $ε$ denotes the thickness of the domain and the roughness periodicity of the boundary. By using an adapted linear unfolding operator we perform a detailed analysis of the asymptotic behavior of the Bingham flow when $ε$ tends to zero. We obtain the homogenized limit problem for the velocity and the pressure, which preserves the nonlinear character of the flow, and study the effects of the microstructure in the corresponding effective equations. Finally, we give the interpretation of the limit problem in terms of a non linear Darcy law.

math.AP↗

arXiv2013

Uniform resolvent convergence for strip with fast oscillating boundary

In a planar infinite strip with a fast oscillating boundary we consider an elliptic operator assuming that both the period and the amplitude of the oscillations are small. On the oscillating boundary we impose Dirichlet, Neumann or Robin boundary condition. In all cases we describe the homogenized operator, establish the uniform resolvent convergence of the perturbed resolvent to the homogenized one, and prove the estimates for the rate of convergence. These results are obtained as the order of the amplitude of the oscillations is less, equal or greater than that of the period. It is shown that under the homogenization the type of the boundary condition can change.

math.AP↗