29 citations · 47 across the 12 of their papers we have counts for
17 papers
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…
Modeling ant foraging: a chemotaxis approach with pheromones and trail formation
Paulo Amorim
We consider a continuous mathematical description of a population of ants and simulate numerically their foraging behavior using a system of partial differential equations of chemo…
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…
A Numerical Approach to Scalar Nonlocal Conservation Laws
Paulo Amorim, Rinaldo M. Colombo, Andreia Teixeira
We address the study of a class of 1D nonlocal conservation laws from a numerical point of view. First, we present an algorithm to numerically integrate them and prove its converge…
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…
Convergence of a numerical scheme for a coupled Schrödinger--KdV system
Paulo Amorim, Mário Figueira
We prove the convergence in a strong norm of a finite difference semi-discrete scheme approximating a coupled Schrödinger--KdV system on a bounded domain. This system models the in…
Convergence of a finite difference method for the KdV and modified KdV equations with data
Paulo Amorim, Mário Figueira
We prove strong convergence of a semi-discrete finite difference method for the KdV and modified KdV equations. We extend existing results to non-smooth data (namely, in ), wi…
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…
Convergence of numerical schemes for short wave long wave interaction equations
Paulo Amorim, Mário Figueira
We consider the numerical approximation of a system of partial differential equations involving a nonlinear Schrödinger equation coupled with a hyperbolic conservation law. This sy…
Computing Gowdy spacetimes via spectral evolution in future and past directions
Paulo Amorim, Christine Bernardi, Philippe G. LeFloch
We consider a system of nonlinear wave equations with constraints that arises from the Einstein equations of general relativity and describes the geometry of the so-called Gowdy sy…
Finite volume schemes on Lorentzian manifolds
Paulo Amorim, Philippe G. LeFloch, Bawer Okutmustur
We investigate the numerical approximation of (discontinuous) entropy solutions to nonlinear hyperbolic conservation laws posed on a Lorentzian manifold. Our main result establishe…
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…