14 citations · 26 across the 9 of their papers we have counts for
11 papers
Optimization of the Steklov-Lamé eigenvalues with respect to the domain
Beniamin Bogosel, Pedro R. S. Antunes
This work deals with theoretical and numerical aspects related to the behavior of the Steklov-Lamé eigenvalues on variable domains. After establishing the eigenstructure for the di…
Numerical calculation of extremal Steklov eigenvalues in 3D and 4D
Pedro R. S. Antunes
We develop a numerical method for solving shape optimization of functionals involving Steklov eigenvalues and apply it to the problem of maximization of the -th Steklov eigenval…
Modelling silicosis: dynamics of a model with piecewise constant rate coefficients
Pedro R. S. Antunes, Fernando P. da Costa, João T. Pinto +1
We study the dynamics about equilibria of an infinite dimension coagulation-fragmentation-death model for the silicosis disease mechanism introduced recently by da Costa, Drmota, a…
A well conditioned Method of Fundamental Solutions
Pedro R. S. Antunes
The method of fundamental solutions (MFS) is a numerical method for solving boundary value problems involving linear partial differential equations. It is well known that it can be…
Bound states in semi-Dirac semi-metals
David Krejcirik, Pedro. R. S. Antunes
New insights into transport properties of nanostructures with a linear dispersion along one direction and a quadratic dispersion along another are obtained by analysing their spect…
A variational formulation for Dirac operators in bounded domains. Applications to spectral geometric inequalities
Pedro R. S. Antunes, Rafael D. Benguria, Vladimir Lotoreichik +1
We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of . Motivated by spectral geometric inequali…
On the behaviour of clamped plates under large compression
P. R. S. Antunes, D. Buoso, P. Freitas
We determine the asymptotic behaviour of eigenvalues of clamped plates under large compression, by relating this problem to eigenvalues of the Laplacian with Robin boundary conditi…
Parametric Shape Optimization using the Support Function
Pedro R. S. Antunes, Beniamin Bogosel
The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate s…
Bounds and extremal domains for Robin eigenvalues with negative boundary parameter
Pedro R. S. Antunes, Pedro Freitas, David Krejcirik
We present some new bounds for the first Robin eigenvalue with a negative boundary parameter. These include the constant volume problem, where the bounds are based on the shrinking…
Critical behaviour for scalar nonlinear waves
Davide Masoero, Andrea Raimondo, Pedro R. S. Antunes
In the long-wave regime, nonlinear waves may undergo a phase transition from a smooth to a fast oscillatory behaviour. We study this phenomenon, commonly known as dispersive shock,…
Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian
Pedro R. S. Antunes, Pedro Freitas, James B. Kennedy
We consider the problem of minimising the eigenvalue of the Robin Laplacian in . Although for and a positive boundary parameter it is known tha…