Welcome to my home page. I am currently a Ciênca 2008 researcher at CMAF (Centro de Matemática e Aplicações Fundamentais) at the University of Lisbon.
I am a member of the team "Hyperbolic Systems and Singularities in PDEs". My email: pvamorim at fc.ul.pt

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Publications These are preprints and links to the journal pages. Subscription may be required. Please see the Arxiv for free access versions of some of these papers.
Some of my preprints and publications are in the Arxiv.

12. 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) (published)

11. The linear stability of shock waves for the nonlinear Schrodinger-Inviscid Burgers system (with M. Figueira, J.-P. Dias and P.G. LeFloch), to appear in Journal of Dynamics and Differential Equations. (2012) preprint, published

10. Convergence of a finite difference method for the KdV and modified KdV equations with $L^2$ data (with M. Figueira), Submitted. pdf

9. Convergence of a numerical scheme for a coupled Schrödinger–KdV system (with M. Figueira), Rev. Mat. Complutense, 2012. (preprint) (published)

8. A nonlinear model describing a short wave long wave interaction in a viscoelastic medium. (with J.-P. Dias), to appear in Quarterly of Applied Mathematics. (2012) (preprint) (published)

7. Convergence of numerical schemes for interaction equations of short and long waves. (with M. Figueira), Journal of Hyperbolic Differential Equations, 8, no. 4 (2011), 777–81. (preprint) (published)

6. A geometric approach to error estimates for conservation laws posed on a spacetime. (with Philippe G. LeFloch and Wladimir Neves), Nonlinear Analysis 74 (2011) 4898-4917 pdf or preprint

5. Convergence of semi-discrete approximations of Benney equations (with M. Figueira), C. R. Acad. Sci. Paris, Ser. I. 347 (2009) 1135-1140 pdf

4. Computing Gowdy spacetimes via spectral evolution in future and past directions (with C. Bernardi and P.G. LeFloch), Class. Quant. Grav. 26:025007, (2009). pdf

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

2. Sharp estimates for periodic solutions to the Euler--Poisson--Darboux equation (with P.G. LeFloch), Port. Math. (65) No. 3, (2008). pdf

1. Hyperbolic conservation laws on manifolds: total variation estimates and the finite volume method (with M. Ben Artzi and P.G. LeFloch), Methods and Applications of Analysis, {12}, No. 3 (2005). pdf

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I have organized the one-day meeting on Hyperbolic PDEs at CMAF on the 21st October 2011.

PhD Thesis: Equations hiperboliques non-linéaires sur les variétés : méthodes de volumes finis et méthodes spectrales (pdf 1.9MB) (July 2008), Laboratoire Jaques-Louis Lions, University of Paris 6. Supervisor: Philippe G. LeFloch.