29 citations · 47 across the 12 of their papers we have counts for
10 papers · 1 filter
A structured model of vector-borne disease with within-host viral load and antibody dynamics
Paulo Amorim, Maria Soledad Aronna, Debora de Oliveira Medeiros
We present an epidemiological model for vector-borne diseases that includes within-host viral load and antibody dynamics using structured transport equations. By incorporating the…
The obstacle problem for scalar conservation laws with nonlocal dynamics
Paulo Amorim, Alexander Keimer, Lukas Pflug +1
In this article, we present a method to find a solution to a one-dimensional nonlocal conservation law that respects a space-dependent mapping, referred to as the obstacle. This is…
Analysis of a chemotaxis system modeling ant foraging
Ricardo Alonso, Paulo Amorim, Thierry Goudon
In this paper we analyze a system of PDEs recently introduced in [P. Amorim, {\it Modeling ant foraging: a {chemotaxis} approach with pheromones and trail formation}], in order to…
The obstacle-mass constraint problem for hyperbolic conservation laws. Solvability
Paulo Amorim, Wladimir Neves, José Francisco Rodrigues
In this work we introduce the obstacle-mass constraint problem for a multidimensional scalar hyperbolic conservation law. We prove existence of an entropy solution to this problem…
A continuous model of ant foraging with pheromones and trail formation
Paulo Amorim
We propose and numerically analyze a PDE model of ant foraging behavior. Ant foraging is a prime example of individuals following simple behavioral rules based on local information…
On a nonlocal hyperbolic conservation law arising from a gradient constraint problem
Paulo Amorim
In some models involving nonlinear conservation laws, physical mechanisms exist which prevent the formation of shocks. This gives rise to conservation laws with a constraint on the…
A nonlinear model describing a short wave long wave interaction in a viscoelastic medium
Paulo Amorim, João-Paulo Dias
In this paper we introduce a system coupling a nonlinear Schrödinger equation with a system of viscoelasticity, modeling the interaction between short and long waves, acting for in…
The linear stability of shock waves for the nonlinear Schrödinger-Inviscid Burgers system
Paulo Amorim, Joao-Paulo Dias, Mario Figueira +1
We investigate the coupling between the nonlinear Schrödinger equation and the inviscid Burgers equation, a system which models interactions between short and long waves, for insta…
A geometric approach to error estimates for conservation laws posed on a spacetime
Paulo Amorim, Philippe G. LeFloch, Wladimir Neves
We consider a hyperbolic conservation law posed on an (N+1)-dimensional spacetime, whose flux is a field of differential forms of degree N. Generalizing the classical Kuznetsov's m…
Hyperbolic Conservation Laws on Manifolds. Total Variation Estimates and the Finite Volume Method
Paulo Amorim, Matania Ben-Artzi, Philippe G. LeFloch
This paper investigates some properties of entropy solutions of hyperbolic conservation laws on a Riemannian manifold. First, we generalize the Total Variation Diminishing (TVD) pr…