Research Publications IM Dep. Mat. UFRJ

Paulo Amorim

Welcome to my home page. I am Professor Associado at Instituto de Matemática - Universidade Federal do Rio de Janeiro.
My email: paulo at

Curriculo Lattes.

Chefe do Departamento de Matemática do IM - UFRJ.

Instituto de Matemática - Universidade Federal do Rio de Janeiro
Instituto de Matemática, UFRJ,
Av. Athos da Silveira Ramos 149,
Centro de Tecnologia - Bloco C,
Cidade Universitária - Ilha do Fundão,
C.P. 68530, 21941-909 Rio de Janeiro,
RJ - Brasil

Sala C127-12


I work in Partial Differential Equations, mathematical biology and hyperbolic conservation laws. I am currently interested in animal motion and ecology models.



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. (submitted),

Accepted and published

23. P. Amorim, T. Goudon, Analysis of a model of self-propelled agents interacting through pheromone. , Nonlinearity 34 6301 (2021) pdf, (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, (pdf), (DOI).

21. P. Amorim, Predator-prey interactions with hunger structure. , (pdf) 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) pdf.

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), pdf.

18. P. Amorim, T. Goudon, F. Peruani, An ant navigation model based on Weber's law. J. Math. Biol. (2019) 78: 943. (journal page), (pdf)

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)

16. R. Alonso, P. Amorim, T. Goudon, Analysis of a chemotaxis system modeling ant foraging. (published pdf file) (preprint) Math. Models Methods Appl. Sci. 26, 1785 (2016) (Journal web page)

15. P. Amorim, Modeling ant foraging: a chemotaxis approach with pheromones and trail formation. Journal of Theoretical Biology 385 (2015) 160--173. (published pdf file) (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) (pdf)

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, pdf

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, pdf

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. pdf, 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, pdf

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, pdf

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, pdf

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, pdf

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, pdf

3.P. Amorim, P.G. LeFloch, B. Okutmustur, Finite volume schemes on Lorentzian manifolds. Comm. Math. Sci. (6) No. 4, (2008). Journal link, pdf

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, pdf

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, pdf