70 citations · 151 across the 19 of their papers we have counts for
22 papers
Selection of the angular speed of rotating waves in segregated reaction-diffusion systems with asymmetric competition
Giuseppe Spadaro, Gianmaria Verzini, Alessandro Zilio
We investigate the existence of segregated rotating waves, arising in the singular limit of competition-diffusion systems of the type \[ \partial_t u_i -\partial_{xx} u_i = f(u_i)-…
A field-road system with a rectifiable set
Matthieu Bonnivard, Romain Ducasse, Antoine Lemenant +1
The aim of this paper is to define a field-road system in 2D where the road is a merely 1D-rectifiable set. For this purpose we introduce a general setting in order to define a par…
A -convergence result for 2D type-I superconductors
Alessandro Cosenza, Michael Goldman, Alessandro Zilio
We consider a 2D non-standard Modica-Mortola type functional. This functional arises from the Ginzburg-Landau theory of type-I superconductors in the case of an infinitely long sam…
Rotating Spirals in segregated reaction-diffusion systems
Ariel Salort, Susanna Terracini, Gianmaria Verzini +1
We give a complete characterization of the boundary traces () supporting spiraling waves, rotating with a given angular speed , which appear as singular limit…
Free boundary problems with long-range interactions: uniform Lipschitz estimates in the radius
Nicola Soave, Hugo Tavares, Alessandro Zilio
Consider the class of optimal partition problems with long range interactions \[ \inf \left\{ \sum_{i=1}^k λ_1(ω_i):\ (ω_1,\ldots, ω_k) \in \mathcal{P}_r(Ω) \right\}, \] where $λ_1…
Parallel dark soliton pair in a bistable 2D exciton-polariton superfluid
Giovanni Lerario, Sergei V. Koniakhin, Anne Maître +7
Collective excitations, such as vortex-antivortex and dark solitons, are among the most fascinating effects of macroscopic quantum states. However, 2D dark solitons are unstable an…
Regularity of all minimizers of a class of spectral partition problems
Hugo Tavares, Alessandro Zilio
We study a rather broad class of optimal partition problems with respect to monotone and coercive functional costs that involve the Dirichlet eigenvalues of the partitions. We show…
Predator-prey models with competition, Part II: uniform regularity estimates
Henri Berestycki, Alessandro Zilio
We study a system of elliptic equations with strong competition and an arbitrary large number of components. The system is related to a model of predators and prey, with a single a…
Predator-prey models with competition, Part III: Classification of stationary solutions
Henri Berestycki, Alessandro Zilio
For a stationary system representing prey and groups of competing predators, we show classification results about the set of positive solutions. In particular, we show that if…
Regularity results for segregated configurations involving fractional Laplacian
Giorgio Tortone, Alessandro Zilio
We study the regularity of segregated profiles arising from competition - diffusion models, where the diffusion process is of nonlocal type and is driven by the fractional Laplacia…
Competition in periodic media: III -- Existence \& stability of segregated periodic coexistence states
Léo Girardin, Alessandro Zilio
In this paper we consider a system of parabolic reaction-diffusion equations with strong competition and two related scalar reaction-diffusion equations. We are mainly concerned wi…
Predators-prey models with competition Part I: existence, bifurcation and qualitative properties
Henri Berestycki, Alessandro Zilio
We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we stu…
Spiraling asymptotic profiles of competition-diffusion systems
Susanna Terracini, Gianmaria Verzini, Alessandro Zilio
This paper describes the structure of the nodal set of segregation profiles arising in the singular limit of planar, stationary, reaction-diffusion systems with strongly competitiv…
Variational problems with long-range interaction
Nicola Soave, Hugo Tavares, Susanna Terracini +1
We consider a class of variational problems for densities that repel each other at distance. Typical examples are given by the Dirichlet functional and the Rayleigh functional \[ D…
Multidimensional entire solutions for an elliptic system modelling phase separation
Nicola Soave, Alessandro Zilio
For the system of semilinear elliptic equations \[ ΔV_i = V_i \sum_{j \neq i} V_j^2, \qquad V_i > 0 \qquad \text{in } \] we devise a new method to construct entire so…
On phase separation in systems of coupled elliptic equations: asymptotic analysis and geometric aspects
Nicola Soave, Alessandro Zilio
We consider a family of positive solutions to the system of components \[ -Δu_{i,β} = f(x, u_{i,β}) - βu_{i,β} \sum_{j \neq i} a_{ij} u_{j,β}^2 \qquad \text{in }, \] where $…
Hölder bounds and regularity of emerging free boundaries for strongly competing Schrödinger equations with nontrivial grouping
Nicola Soave, Hugo Tavares, Susanna Terracini +1
We study regularity issues for systems of elliptic equations of the type \[ -Δu_i=f_{i,β}(x)-β\sum_{j\neq i} a_{ij} u_i |u_i|^{p-1}|u_j|^{p+1} \] set in domains $Ω\subset \mathbb{R…
Uniform bounds for strongly competing systems: the optimal Lipschitz case
Nicola Soave, Alessandro Zilio
For a class of systems of semi-linear elliptic equations, including \[ -Δu_i=f_i(x,u_i) - βu_i\sum_{j\neq i}a_{ij}u_j^p,\qquad i=1,\dots,k, \] for (variational-type interacti…
Strong competition versus fractional diffusion: the case of Lotka-Volterra interaction
Gianmaria Verzini, Alessandro Zilio
We consider a system of differential equations with nonlinear Steklov boundary conditions, related to the fractional problem $$(-Δ)^s u_i = f_i(x,u_i) - βu_i^p \sum_{j\neq i} a_{ij…
Uniform Hölder regularity with small exponent in competition-fractional diffusion systems
Susanna Terracini, Gianmaria Verzini, Alessandro Zilio
For a class of competition-diffusion nonlinear systems involving fractional powers of the Laplacian, including as a special case the fractional Gross-Pitaevskii system, we prove th…
Entire solutions with exponential growth for an elliptic system modeling phase-separation
Nicola Soave, Alessandro Zilio
We prove the existence of entire solutions with exponential growth for the semilinear elliptic system [\begin{cases} -Δu = -u v^2 & \text{in } -Δv= -u^2 v & \text{in }…
Uniform Holder bounds for strongly competing systems involving the square root of the laplacian
Susanna Terracini, Gianmaria Verzini, Alessandro Zilio
For a class of competition-diffusion nonlinear systems involving the square root of the Laplacian, including the fractional Gross-Pitaevskii system, we prove that uniform boundedne…