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Pedro Alves Martins da Silva Girão. Concluiu o(a) Licenciatura em Licenciatura em Engenharia Electrotécnica e Computadores em 1987 pelo(a) Universidade de Lisboa Instituto Superior Técnico e Doctor of Philosophy em Matemática em 1993/01 pelo(a) New York University Courant Institute of Mathematical Sciences. É Professor Associado no(a) Universidade de Lisboa Instituto Superior Técnico Departamento de Matemática, Professor Associado no(a) Universidade de Lisboa Instituto Superior Técnico e Professor Associado no(a) Centro de Análise Matemática Geometria e Sistemas Dinâmicos. Atua na(s) área(s) de Ciências Exatas com ênfase em Matemática.
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Identification

Personal identification

Full name
Pedro Alves Martins da Silva Girão

Citation names

  • Pedro Girão
  • Pedro Martins Girão
  • Pedro M. Girão

Author identifiers

Ciência ID
7A1B-3BEA-8C8A
ORCID iD
0000-0001-6799-9478
Google Scholar ID
https://scholar.google.pt/citations?user=AB9LIowAAAAJ&hl=en&authoruser=1
Researcher Id
L-5985-2013
Scopus Author Id
35570267500

Email addresses

  • pgirao@math.ist.utl.pt (Professional)

Telephones

Telephone
  • (+351) 218417101 (Professional)

Addresses

  • Departamento de Matemática, Instituto Superior Técnico. Avenida Rovisco Pais, 1049-001, Lisboa, Lisboa, Portugal (Professional)

Websites

Knowledge fields

  • Exact Sciences - Mathematics
Education
Degree Classification
1988 - 1993
Concluded
 Mathematics (Doctor of Philosophy)
New York University Courant Institute of Mathematical Sciences, United States
1982 - 1987/01
Concluded
 Engenharia Electrotécncia e de Computadores (Licenciatura)
Universidade de Lisboa Instituto Superior Técnico, Portugal
 18
Affiliation

Teaching in Higher Education

Category
Host institution 		Employer
2008/04 - Current Associate Professor (University Teacher) Universidade de Lisboa Instituto Superior Técnico, Portugal
Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Portugal
(...)
1993/06 - 2008/04 Assistant Professor (University Teacher) Universidade de Lisboa Instituto Superior Técnico, Portugal
Projects

Contract

Designation Funders
2016/01/01 - 2019/06/30 Global properties of solutions of the Einstein equations
PTDC/MAT-ANA/1275/2014
Researcher
Ongoing
2013/07/01 - 2015/09/30 Advances in nonlinear pdes: from degenerate equations to stochastic control and mean-field games
info:eu-repo/grantAgreement/FCT/COMPETE/125354/PT
Researcher
Fundação para a Ciência e a Tecnologia
Concluded
2011/08/10 - 2014/08/09 Degenerate elliptic and parabolic equations and its applications to front propagation
info:eu-repo/grantAgreement/FCT/3599-PPCDT/110759/PT
Researcher
Fundação para a Ciência e a Tecnologia
Concluded
2011/04/01 - 2014/03/31 Non-linear degenerate elliptic equations and systems
info:eu-repo/grantAgreement/FCT/3599-PPCDT/114397/PT
Researcher
Fundação para a Ciência e a Tecnologia
Concluded
2007/10/01 - 2014/03/30 Analysis of Nonlinear Partial Differential Equations
info:eu-repo/grantAgreement/RCUK/EPSRC/EP2%FE0350272%F1/GB
Researcher
Fundação para a Ciência e a Tecnologia
Concluded
2010/04/04 - 2012/10/03 Analysis of the Einstein Equations
info:eu-repo/grantAgreement/FCT/5876-PPCDTI/108921/PT
Researcher
Fundação para a Ciência e a Tecnologia
Concluded
2007/01/01 - 2009 Analysis and Applications of Partial Differential Equations
info:eu-repo/grantAgreement/FCT/3599-PPCDT/82689/PT
Researcher
Fundação para a Ciência e a Tecnologia
Concluded
1996 - 1999 Análise Não-Linear e Sistemas Dinâmicos
PRAXIS 2/2.1/MAT/199/94
Researcher
Concluded
1996 - 1998 Transições de Fase e Equações Diferenciais Parciais
JNICT PBIC c Mat 2139/95
Researcher
Concluded
Outputs

Publications

Book
  1. Girão, Pedro. Introdução à Análise Complexa, Séries de Fourier e Equações Diferenciais. Lisboa, Portugal: IST Press. 2014.
    Published
Book chapter
  1. Girão, Pedro Martins; Kohn, Robert V.. "The Crystalline Algorithm for Computing Motion by Curvature". In Variational Methods for Discontinuous Structures, 7-18. Birkhäuser Basel, 1996.
    10.1007/978-3-0348-9244-5_2
Journal article
  1. Costa, João L.; Girão, Pedro M.. "Higher order linear stability and instability of Reissner–Nordström’s Cauchy horizon". Analysis and Mathematical Physics 10 3 (2020): http://dx.doi.org/10.1007/s13324-020-00380-5.
    10.1007/s13324-020-00380-5
  2. Girão, Pedro M; Natário, José; Silva, Jorge Drumond. "Solutions of the wave equation bounded at the Big Bang". Classical and Quantum Gravity 36 7 (2019): 075016. http://dx.doi.org/10.1088/1361-6382/ab09b2.
    10.1088/1361-6382/ab09b2
  3. Costa, João L.; Girão, Pedro M.; Natário, José; Silva, Jorge Drumond. "On the Occurrence of Mass Inflation for the Einstein–Maxwell-Scalar Field System with a Cosmological Constant and an Exponential Price Law". Communications in Mathematical Physics 361 1 (2018): 289-341. http://dx.doi.org/10.1007/s00220-018-3122-z.
    10.1007/s00220-018-3122-z
  4. Costa, João L.; Girão, Pedro M.; Natário, José; Silva, Jorge Drumond. "On the Global Uniqueness for the Einstein–Maxwell-Scalar Field System with a Cosmological Constant: Part 3. Mass Inflation and Extendibility of the Solutions". Annals of PDE 3 1 (2017): http://dx.doi.org/10.1007/s40818-017-0028-6.
    10.1007/s40818-017-0028-6
  5. Costa, João L.; Girão, Pedro M.; Natário, José; Silva, Jorge Drumond. "On the Global Uniqueness for the Einstein–Maxwell-Scalar Field System with a Cosmological Constant. Part 2: Structure of the solutions and stability of the Cauchy horizon". Communications in Mathematical Physics 339 3 (2015): 903-947. http://dx.doi.org/10.1007/s00220-015-2433-6.
    10.1007/s00220-015-2433-6
  6. Costa, João L; Girão, Pedro M; Natário, José; Silva, Jorge Drumond. "Cauchy horizon stability and mass inflation with a cosmological constant". Journal of Physics: Conference Series 600 (2015): 012031. http://dx.doi.org/10.1088/1742-6596/600/1/012031.
    10.1088/1742-6596/600/1/012031
  7. Costa, João L; Girão, Pedro M; Natário, José; Silva, Jorge Drumond. "On the global uniqueness for the Einstein–Maxwell-scalar field system with a cosmological constant. Part 1: Well posedness and breakdown criterion". Classical and Quantum Gravity 32 1 (2014): 015017. http://dx.doi.org/10.1088/0264-9381/32/1/015017.
    10.1088/0264-9381/32/1/015017
  8. Girão, Pedro Martins; Pérez-Llanos, Mayte. "Bifurcation curves of a diffusive logistic equation with harvesting orthogonal to the first eigenfunction". Journal of Mathematical Analysis and Applications 403 2 (2013): 376-390. http://dx.doi.org/10.1016/j.jmaa.2013.02.015.
    10.1016/j.jmaa.2013.02.015
  9. Girão, Pedro Martins. "Bifurcation curves of a logistic equation when the linear growth rate crosses a second eigenvalue". Nonlinear Analysis: Theory, Methods & Applications 74 1 (2011): 94-113. http://dx.doi.org/10.1016/j.na.2010.08.020.
    10.1016/j.na.2010.08.020
  10. Girão, Pedro; Tehrani, Hossein. "On the Fucik spectrum of the wave operator and an asymptotically linear problem". Journal of Mathematical Analysis and Applications 366 1 (2010): 55-66. http://dx.doi.org/10.1016/j.jmaa.2009.12.031.
    10.1016/j.jmaa.2009.12.031
  11. Girão, Pedro M.; Gomes, José Maria. "Multibump nodal solutions for an indefinite superlinear elliptic problem". Journal of Differential Equations 247 4 (2009): 1001-1012. http://dx.doi.org/10.1016/j.jde.2009.04.018.
    10.1016/j.jde.2009.04.018
  12. Girão, Pedro M.; Gomes, José Maria. "Multi-bump nodal solutions for an indefinite non-homogeneous elliptic problem". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 139 4 (2009): 797-817. http://dx.doi.org/10.1017/s0308210508000474.
    10.1017/s0308210508000474
  13. Girão, Pedro; Tehrani, Hossein. "Positive solutions to logistic type equations with harvesting". Journal of Differential Equations 247 2 (2009): 574-595. http://dx.doi.org/10.1016/j.jde.2009.02.008.
    10.1016/j.jde.2009.02.008
  14. Girão, Pedro; Weth, Tobias. "The shape of extremal functions for Poincaré–Sobolev-type inequalities in a ball". Journal of Functional Analysis 237 1 (2006): 194-223. http://dx.doi.org/10.1016/j.jfa.2006.01.001.
    10.1016/j.jfa.2006.01.001
  15. Chabrowski, Jan; Girao, Pedro M.. "On the exterior Neumann problem involving the critical Sobolev exponent". Topological Methods in Nonlinear Analysis 23 1 (2004): 33. http://dx.doi.org/10.12775/tmna.2004.002.
    10.12775/tmna.2004.002
  16. Costa, David G.; Girão, Pedro M.. "Existence and nonexistence of least energy solutions of the Neumann problem for a semilinear elliptic equation with critical Sobolev exponent and a critical lower-order perturbation". Journal of Differential Equations 188 1 (2003): 164-202. http://dx.doi.org/10.1016/s0022-0396(02)00070-0.
    10.1016/s0022-0396(02)00070-0
  17. Girão, Pedro. "A family of sharp inequalities for Sobolev functions". Adv. Differential Equations 8 6 (2003): 641-671. https://projecteuclid.org/euclid.ade/1355926830.
    Published
  18. Chabrowski, Jan; Girao, Pedro M.. "Symmetric solutions of the Neumann problem involving a critical Sobolev exponent". Topological Methods in Nonlinear Analysis 19 1 (2002): 1. http://dx.doi.org/10.12775/tmna.2002.001.
    10.12775/tmna.2002.001
  19. Girão, Pedro M. "A sharp inequality for Sobolev functions". Comptes Rendus Mathematique 334 2 (2002): 105-108. http://dx.doi.org/10.1016/s1631-073x(02)02215-x.
    10.1016/s1631-073x(02)02215-x
  20. Girão, Pedro; Ramos, Miguel. "Sign changing solutions for elliptic equations with critical growth in cylinder type domains". ESAIM: Control, Optimisation and Calculus of Variations 7 (2002): 407-419. http://dx.doi.org/10.1051/cocv:2002061.
    10.1051/cocv:2002061
  21. Chabrowski, J.; Girão, P. M.. "The nonlinear Neumann problem and sharp weighted Sobolev inequalities". Colloquium Mathematicum 88 2 (2001): 193-213. http://dx.doi.org/10.4064/cm88-2-3.
    10.4064/cm88-2-3
  22. Girão, Pedro Martins. "Convergence of a Crystalline Algorithm for the Motion of a Simple Closed Convex Curve by Weighted Curvature". SIAM Journal on Numerical Analysis 32 3 (1995): 886-899. http://dx.doi.org/10.1137/0732041.
    10.1137/0732041
  23. Girão, Pedro Martins; Kohn, Robert V.. "Convergence of a crystalline algorithm for the heat equation in one dimension and for the motion of a graph by weighted curvature". Numerische Mathematik 67 1 (1994): 41-70. http://dx.doi.org/10.1007/s002110050017.
    10.1007/s002110050017
Activities

Supervision

Thesis Title
Role 		Degree Subject (Type)
Institution / Organization
2023/02/15 - 2023/07/15 The effects of a delta distribution in simple quantum mechanical potentials
Co-supervisor
Universidade de Lisboa Instituto Superior Técnico, Portugal
2023/02/15 - 2023/07/15 Lorentz and Möbius transformations, and the relativity of the observed sky
Co-supervisor
Universidade de Lisboa Instituto Superior Técnico, Portugal
2016/12/01 - 2022/06/30 Regularity of a double null coordinate system for Kerr-Newman-de Sitter spacetimes
Co-supervisor
Universidade de Lisboa Instituto Superior Técnico, Portugal
2017/09/30 - 2018/07/15 The vector field method for bounding energy waves inside black holes
Supervisor
Universidade de Lisboa Instituto Superior Técnico, Portugal
2016/02/15 - 2016/07/15 Klein-Gordon equations
Supervisor
Universidade de Lisboa Instituto Superior Técnico, Portugal
2010/02/01 - 2010/08/01 Bifurcation curves of a diffusive logistic equation with harvesting orthogonal to the first eigenfunction
Supervisor
Universidade de Lisboa Instituto Superior Técnico, Portugal
2006/12/01 - 2007/11/06 Multibump nodal solutions for an indefinite nonhomogeneous elliptic problems
Supervisor
Universidade de Lisboa Instituto Superior Técnico, Portugal
Distinctions

Award

1993 SIAM Student Paper Prize
Society for Industrial and Applied Mathematics, United States
1987 Prémio Marconi