Prof. Dr. Juan J. L. Velázquez

E-mail: velazquez(at)
Phone: +49 228 73 62378
Room: 2.023
Location: Mathematics Center
Institute: Institute for Applied Mathematics
Research Areas: Research Area C1
Interdisciplinary Research Unit D3-5

Academic Career


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

Research Profile

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.

Research Projects and Activities

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”

Publication List

MathSciNet Publication List (external link)

ArXiv Preprint List (external link)


• SIAM Journal on Mathematical Analysis (2001 - 2005)
• Revista Matemática Iberoamericana (2001 - 2008)



A. v. Humboldt-J. C. Mutis Research Award (Alexander von Humboldt Foundation)

Selected Invited Lectures


Keynote speaker, Equadiff Congress, Berlin


PDE session, International Congress of Mathematicians, Madrid, Spain


Keynote speaker, Equadiff Congress, Vienna, Austria

Selected PhD students

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

Supervised Theses

  • Master theses: 6
  • PhD theses: 5, currently 2
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