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| 1990 | PhD, Mathematics, Complutense University of Madrid, Spain | | 1991 - 1992 | Postdoctoral stay, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN, USA | | 1992 - 1997 | Associate Professor, Applied Mathematics Department, Complutense University of Madrid, Spain | | 1997 - 2008 | Professor, Applied Mathematics Department, Complutense University of Madrid, Spain | | 2008 - 2011 | Research Professor, Institute of Mathematical Sciences (ICMAT), Spanish National Research Council (CSIC), Madrid, Spain | | Since 2011 | Professor (W3), University of Bonn |
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My field of expertise is the analysis of Partial Differential Equations. In particular, I have been concerned with the study of singularities arising in Nonlinear Differential Equations and the study of the asymptotic behaviour of their solutions in a neighbourhood of the singular points.
My main current research interests is the study of several equations arising in Kinetic Theory. Specific equations in which I have worked recently are in the study of the bosonic Nordheim-Boltzmann equation, the kinetic equations describing Wave Turbulence, and coagulation equations. Some problems which I have studied about these models are the onset of singularities in finite time, the construction of self-similar behaviour which describe the long time asymptotics of the solutions of some of these equations and to determine if they are unique. I am also interested in the study of coarsening models for systems of particles interacting by means of short range potentials, in the study of screening effects in many particle systems and in the study of the properties of large chemical networks as the ones which arise often in problems of Mathematical Biology.
Concerning my future resarch plans, besides continuing with the study of the properties of the Kinetic Models mentioned above, I am interested in understanding the precise connection between the kinetic equations and the underlying particle systems which the equations are expected to approximate. Some specific problems which I intend to address in the future include the study of the mechanical properties of systems described by the Boltzmann equation and the analysis of systems with long range interactions. I am also interested in understanding possible oscillatory behaviours arising in Smoluchowski equations, as well as in the study of coarsening models interacting by means of short range potentials for which might be possible to prove rigorously that the distribution of particle sizes behaves in a probabilistic manner.
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Responsible of two grants of the Spanish Government about “Partial Differential Equations in Mathematical Physics”
2004 - 2007 and 2007 - 2010
Collaborative Research Center SFB 1060 “The mathematics of emergent effects”
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[ 1] Miguel A. Herrero, Juan J. L. Velazquez
Singularity patterns in a chemotaxis model
Math. Ann. , 306: (3): 583--623
1996
DOI: 10.1007/BF01445268[ 2] J. J. L. Velazquez
Point dynamics in a singular limit of the Keller-Segel model. I. Motion of the concentration regions
SIAM J. Appl. Math. , 64: (4): 1198--1223
2004
DOI: 10.1137/S0036139903433888[ 3] M. Escobedo, S. Mischler, J. J. L. Velazquez
On the fundamental solution of a linearized Uehling-Uhlenbeck equation
Arch. Ration. Mech. Anal. , 186: (2): 309--349
2007
DOI: 10.1007/s00205-007-0084-2[ 4] S. Luckhaus, Y. Sugiyama, J. J. L. Velazquez
Finite time blow-up and condensation for the bosonic Nordheim equation
Arch. Rat. Mech. Anal. , 206: : 31-80
2012[ 5] M. Escobedo, J. J. L. Velazquez
Finite time blow-up and condensation for the bosonic Nordheim equation
Invent. Math. , 200: (3): 761--847
2015
DOI: 10.1007/s00222-014-0539-7[ 6] M. Escobedo, J. J. L. Velazquez
On the theory of weak turbulence for the nonlinear Schrödinger equation
Mem. Amer. Math. Soc. , 238: (1124): v+107
2015
ISBN: 978-1-4704-1434-4; 978-1-4704-2611-8
DOI: 10.1090/memo/1124[ 7] B. Niethammer, J. J. L. Velazquez
Self-similar solutions with fat tails for Smoluchowski's coagulation equation with locally bounded kernels
Comm. Math. Phys. , 318: (2): 505--532
2013
DOI: 10.1007/s00220-012-1553-5[ 8] A. H. M. Kierkels, J. J. L. Velazquez
On self-similar solutions to a kinetic equation arising in weak turbulence theory for the nonlinear Schrödinger equation
J. Stat. Phys. , 163: (6): 1350--1393
2016
DOI: 10.1007/s10955-016-1505-0[ 9] B. Niethammer, S. Throm, J. J. L. Velazquez
Self-similar solutions with fat tails for Smoluchowski's coagulation equation with singular kernels
Ann. Inst. H. Poincaré Anal. Non Linéaire , 33: (5): 1223--1257
2016
DOI: 10.1016/j.anihpc.2015.04.002[ 10] Michael Helmers, Barbara Niethammer, Juan J. L. Velazquez
Mathematical analysis of a coarsening model with local interactions
J. Nonlinear Sci. , 26: (5): 1227--1291
2016
DOI: 10.1007/s00332-016-9304-y |
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• SIAM Journal on Mathematical Analysis (2001 - 2005)
• Revista Matemática Iberoamericana (2001 - 2008)
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| 2005 | A. v. Humboldt-J. C. Mutis Research Award (Alexander von Humboldt Foundation) |
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| 1999 | Keynote speaker, Equadiff Congress, Berlin | | 2006 | PDE session, International Congress of Mathematicians, Madrid, Spain | | 2007 | Keynote speaker, Equadiff Congress, Vienna, Austria |
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Marco A. Fontelos (1997): “Problemas de frontera libre para fluidos viscosos”,
now Professor (on leave), Autonomous University of Madrid, and Researcher, Spanish National Research Council (CISC), Spain
Gerardo Oleaga (2000): “Dinámica de fracturas”,
now Professor (Profesor Contratado Doctor), Complutense University of Madrid, Spain
María Vela (2011): “Ant foraging and minimal paths in simple graphs”,
now Professor, Universidad Europea de Madrid, Spain
Arthur Kierkels (2016): “On a kinetic equation arising in weak turbulence theory for the nonlinear Schrödinger equation”
Raphael Winter
Richard Höfer
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- Master theses: 6
- PhD theses: 5, currently 2
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