I am Associate professor at FGV-EMAp (School of Applied Mathematics, Fundação Getúlio Vargas, Rio de Janeiro) since November 2023. In 2002 I obtained a degree in Mathematics from the University of Lisbon, and a Master's degree in Mathematics in 2005 from the same institution. In 2008 I received a PhD in Mathematics from the Université Paris 6 - Pierre et Marie Curie (today the Sorbonne Université). From 2008 to 2013 I was a Postdoctoral Fellow and Researcher "Ciência 2008" at the Center for Mathematics and Fundamental Applications at the University of Lisbon, and in 2013 I joined the Federal University of Rio de Janeiro as a Professor. I have experience in the areas of Partial Differential Equations, in particular in their applications to Biology and Ecology, and in Hyperbolic Conservation Laws.
Accepted and published publications:
28. P. Amorim, R. de Lima, B. Telch, An ant territory formation model with chemotaxis and alarm pheromones. To appear in Mathematical Biosciences.
27. P. Amorim, J.B. Casteras, J.P. Dias, On the Existence and Partial Stability of Standing Waves for a Nematic Liquid Crystal Director Field Equations. Milan J. Math. 92, 143–167 (2024). Link
26. P. Amorim, A. Margheri, C. Rebelo, Modeling disease awareness and variable susceptibility with a structured epidemic model. Networks and Heterogeneous Media, 19(1): 262–290 (2024). Link, PDF.
25. P. Amorim, J.P. Dias, A.F. Martins, On the motion of the director field of a nematic liquid crystal submitted to a magnetic field and a laser beam. Partial Differential Equations and Applications (2023) 4:36, link.
24. P. Amorim, R. Bürger, R. Ordoñez, L. Villada , Global existence in a food chain model consisting of two competitive preys, one predator and chemotaxis. Nonlinear Analysis: Real World Applications 69 (2023) 103703. link.
23. P. Amorim, T. Goudon, Analysis of a model of self-propelled agents interacting through pheromone. , Nonlinearity 34 6301 (2021) (DOI).
22. P. Amorim, B. Telch, A chemotaxis predator-prey model with indirect pursuit-evasion dynamics and parabolic signal. Journal of Mathematical Analysis and Applications, 500, (1), 2021, 125128, (DOI).
21. P. Amorim, Predator-prey interactions with hunger structure. , SIAM J. Appl. Math., 80(6), 2631-2656 (2020). (DOI)
20. P. Amorim, F. Berthelin, T. Goudon, A nonlocal conservation law describing navigation processes. Journal of Hyperbolic Differential Equations, Vol. 17, No. 04, pp. 809-841 (2020).(DOI)
19. P. Amorim, B. Telch, L.M. Villada, A reaction-diffusion predator-prey model with pursuit, evasion, and nonlocal sensing. Mathematical Biosciences and Engineering, 16(5): 5114–5145 (2019). (journal page)
18. P. Amorim, T. Goudon, F. Peruani, An ant navigation model based on Weber's law. J. Math. Biol. (2019) 78: 943. (journal page)
17. P. Amorim, W. Neves, J.F. Rodrigues, The obstacle-mass constraint problem for hyperbolic conservation laws. Solvability. Annales de l'Institut Henri Poincare / Analyse non lineaire. Vol. 34 (1) p. 221-248 (2017) (published) (preprint)
15. P. Amorim, Modeling ant foraging: a chemotaxis approach with pheromones and trail formation. Journal of Theoretical Biology 385 (2015) 160--173. (preprint) (Journal web page)
14a. P. Amorim, A continuous model of ant foraging with pheromones and trail formation Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, v. 3, n. 1 (2015): CNMAC 2014 (preprint) (published)
14. P. Amorim, R.M. Colombo, A. Teixeira, On the numerical integration of scalar nonlocal conservation laws. M2AN 49, 19--37 (2015). (preprint) (journal link)
13. P. Amorim, S.N. Antontsev, Young measure solutions for the wave equation with p(x,t)-Laplacian: Existence and blow-up Nonlinear Analysis: Theory, Methods and Applications 92, 153-167 (2013) journal link
12. P. Amorim, J.P. Dias, M. Figueira, P.G. LeFloch, The linear stability of shock waves for the nonlinear Schrodinger-Inviscid Burgers system. Journal of Dynamics and Differential Equations. Volume 25, Issue 1, pp 49-69 (2013) preprint, Journal link
11. P. Amorim, M. Figueira, Convergence of a finite difference method for the KdV and modified KdV equations with $L^2$ data. Port. Math., Volume 70, Issue 1 (2013). pdf
10. P. Amorim, M. Figueira, Convergence of a numerical scheme for a coupled Schrodinger-KdV system. Rev. Mat. Complutense, Volume 26, Issue 2, pp 409-426 (2013) (preprint) Journal link
9. P. Amorim, J.P. Dias, A nonlinear model describing a short wave long wave interaction in a viscoelastic medium. Quarterly of Applied Mathematics, 71 (2013), 417-432. Journal link,
8.. P. Amorim, On a nonlocal hyperbolic conservation law arising from a gradient constraint problem. Bulletin of the Brazilian Mathematical Society, Volume 43, Issue 4, pp 599-614 (2012). (preprint) Journal link
7. P. Amorim, M. Figueira, Convergence of numerical schemes for short wave long wave interaction equations Journal of Hyperbolic Differential Equations, 8, no. 4 (2011), 777-81. Journal link
6.P. Amorim, P.G. LeFloch, W. Neves, A geometric approach to error estimates for conservation laws posed on a spacetime. Nonlinear Analysis 74 (2011) 4898-4917 Journal link
5. P. Amorim, M. Figueira, Convergence of semi-discrete approximations of Benney equations. C. R. Acad. Sci. Paris, Ser. I. 347 (2009) 1135-1140 Journal link
4. P. Amorim, C. Bernardi, P.G. LeFloch, Computing Gowdy spacetimes via spectral evolution in future and past directions. Class. Quant. Grav. 26:025007, (2009). Journal link
3.P. Amorim, P.G. LeFloch, B. Okutmustur, Finite volume schemes on Lorentzian manifolds. Comm. Math. Sci. (6) No. 4, (2008). Journal link
2.P. Amorim, P.G. LeFloch, Sharp estimates for periodic solutions to the Euler--Poisson--Darboux equation. Port. Math. (65) No. 3, (2008). Journal link
1.P. Amorim, P.G. LeFloch, M. Ben Artzi, Hyperbolic conservation laws on manifolds: total variation estimates and the finite volume method. Methods and Applications of Analysis, {12}, No. 3 (2005). Journal link