Projects

• Asymptotic behaviour of the positive solutions to semilinear parabolic systems 

• Mathematical modelling of the time-evolution of Alzheimer disease

• Dissipative Maxwell systems with indefinite coefficients

• Helmholtz resonators and geometrically induced scattering resonances

• Thin domain analysis for systems

• Hypocoercivity, semigroups, and the linearised Navier-Stokes system

• Norm resolvent convergence in varying Hilbert spaces

• Hadamard formulae for Maxwell and shape optimization

In preparation

• Spectral analysis of 3x3 J-self-adjoint block operator matrices, with C. Tretter, in preparation, 46pp.

• On the spectrum of a dissipative Maxwell system in the presence of Faraday layers, with M. Marletta,  in preparation, 36pp.

• The Neumann bilaplacian on fattened graphs: eigenvalues asymptotics, with L. Provenzano, in preparation. 

• Eigenvalues of the Maxwell system on product manifolds and thin tubular neighbourhoods, with L. Provenzano,  D. Buoso, in preparation. 

• Pseudospectral properties of the Maxwell system with indefinite conductivity, with L. Boulton, M. Capoferri, in preparation.

Submitted

• Spectral convergence for the Reissner-Mindlin system in arbitrary dimension, with D. Buoso, submitted, 28pp.

Published

1. Essential spectrum for dissipative Maxwell equations in domains with cylindrical ends, with M. Marletta, published online in Journal of Mathematical Analysis and Applications, 19pp, DOI: https://doi.org/10.1016/j.jmaa.2024.128174, 2024.

2.   On the eigenvalues of the biharmonic operator on a thin set with Neumann boundary conditions, with L. Provenzano,  Bulletin of the London Mathematical Society,  55(3), pp. 1154--1177,  https://doi.org/10.1112/blms.12781,  2023.

3.   On a Steklov spectrum in electromagnetics, with P.D. Lamberti, I.G. Stratis, 25 pp., contributed chapter in the book `Adventures in Contemporary Electromagnetic Theory',  editors:  Mackay T.G. and Lakhtakia A., 2023.

4.  Spectral analysis and domain truncation for Maxwell's equations, with S. Bögli, M. Marletta, C. Tretter, Journal de Mathématiques Pures et Appliquées, Vol 170, 96-135, DOI: doi.org/10.1016/j.matpur.2022.12.004, 2023.

5.  Spectral properties of the inhomogeneous Drude-Lorentz model with dissipation, with M. Marletta, Journal of Differential Equations 346, Pages 313-346, DOI: https://doi.org/10.1016/j.jde.2022.11.052, 2023.

6.  On the spectral instability for weak intermediate triharmonic problems,  Math. Methods Appl. Sci. 45, no. 10, 5864-5891, doi:10.1002/mma.8144 , 2022.

7.  On a Babuška paradox for polyharmonic operators: spectral stability and boundary homogenization for intermediate problems , with P.D. Lamberti, Integral Equations Operator Theory,  no. 6, Paper No. 55, 42 pp., https://doi.org/10.1007/s00020-019-2552-0, 2019.

8.  Boundary homogenization for a triharmonic intermediate problem, with J.M. Arrieta, P.D. Lamberti,  Math. Methods Appl. Sci. 41, no. 3, 979–985, doi: 10.1002/mma.4025,  2018.

9.  Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains, with J.M. Arrieta, P.D. Lamberti, Integral Equations Operator Theory 89, no. 3, 377–408, https://doi.org/10.1007/s00020-017-2391-9, 2017.

10.  Singular perturbation Dirichlet problem in a double-periodic perforated plane, with J. Taskinen,  Ann. Univ. Ferrara Sez. VII Sci. Mat. 61, no. 2, 277–290, https://doi.org/10.1007/s11565-014-0222-3, 2015.

Theses

• On the spectral stability of polyharmonic operators on singularly perturbed domains, PhD thesis, 2018

• Singular perturbation problems for a class of partial differential equations in a double-periodic perforated plane, MSc thesis, 2014

• L’ equazione del p-laplaciano: un problema non lineare agli autovalori  [The p-Laplace equation: a non-linear eigenvalue problem], BSc thesis, 2012