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16 papers · 2 filters
Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner
Lucas Chesnel, Xavier Claeys, Sergei A. Nazarov
We investigate the eigenvalue problem in a 2D domain divided into two regions . We are interested in situations where …
Notes on a PDE System for Biological Network Formation
Jan Haskovec, Peter Markowich, Benoit Perthame +1
We present new analytical and numerical results for the elliptic-parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological…
Nonlinear stability criteria for the HMF Model
Mohammed Lemou, Ana Maria Luz, Florian Mehats
We study the nonlinear stability of a large class of inhomogeneous steady state solutions to the Hamiltonian Mean Field (HMF) model. Under a simple criterion, we prove the nonlinea…
Conformal mapping for cavity inverse problem: an explicit reconstruction formula
Alexandre Munnier, Karim Ramdani
In this paper, we address a classical case of the Calderón (or conductivity) inverse problem in dimension two. We aim to recover the location and the shape of a single cavity (…
Bounded correctors in almost periodic homogenization
Scott Armstrong, Antoine Gloria, Tuomo Kuusi
We show that certain linear elliptic equations (and systems) in divergence form with almost periodic coefficients have bounded, almost periodic correctors. This is proved under a n…
On the electrostatic Born-Infeld equation with extended charges
Denis Bonheure, Pietro d'Avenia, Alessio Pomponio
In this paper, we deal with the electrostatic Born-Infeld equation \begin{equation}\label{eq:BI-abs} \tag{} \left\{ \begin{array}{ll} -\operatorname{div}\left(\displa…