

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 


My research area is the study of partial differential equations, in particular I am interested in the analysis of problems motivated by applications in Physics and Biology. In particular, I am interested in the study of models of cellular aggregation induced by chemotaxis (cf. [10], [2], [3]). In recent times I become interested in the study of aggregation of biological organisms induced by nondiffusive cell to cell interactions (cf. [6], [4]).
I am also interested in the study of kinetic equations with particle fluxes between the different regions of the phase space characterizing the system (cf. [9], [8]).


Responsible of two grants of the Spanish Government about “Partial Differential Equations in Mathematical Physics”
2004  2007 and 2007  2010


Research Area B One of my research directions is the study of pattern formation, in particular aggregation patterns in biological systems (cf. [1], [2], [3]). In these papers questions related to the formation of singularities for classical models describing chemotaxis in biological systems. Recently, I have studied the patterns that arise in models in which the interactions between organisms take place by means of local signals (cf. [4], [5], [6]).
I am also interested in the study of coagulation models as well as kinetic models with fluxes of particles between different regions of the phase space. Wellposedness results for coagulation equations as well as for the quantum Boltzmann equation can be found in [7], [8], [9], as well as in other forthcoming papers. 


[ 1] Miguel A. Herrero, Juan J. L. Velázquez
Singularity patterns in a chemotaxis model Math. Ann. , 306: (3): 583623 1996 ISSN: 00255831 DOI: 10.1007/BF01445268[ 2] J. J. L. Velázquez
Point dynamics in a singular limit of the KellerSegel model. I. Motion of the concentration regions SIAM J. Appl. Math. , 64: (4): 11981223 (electronic) 2004 ISSN: 00361399 DOI: 10.1137/S0036139903433888[ 3] Elio Eduardo Espejo Arenas, Angela Stevens, Juan J. L. Velázquez
Simultaneous finite time blowup in a twospecies model for chemotaxis Analysis (Munich) , 29: (3): 317338 2009 ISSN: 01744747 DOI: 10.1524/anly.2009.1029[ 4] A. Stevens, J. J. L. Velázquez
Partial differential equations and nondiffusive structures Nonlinearity , 21: (12): T283T289 2008 ISSN: 09517715 DOI: 10.1088/09517715/21/12/T04[ 5] Kyungkeun Kang, Benoit Perthame, Angela Stevens, J. J. L. Velázquez
An integrodifferential equation model for alignment and orientational aggregation J. Differential Equations , 246: (4): 13871421 2009 ISSN: 00220396 DOI: 10.1016/j.jde.2008.11.006[ 6] Kyungkeun Kang, Angela Stevens, Juan J. L. Velázquez
Qualitative behavior of a KellerSegel model with nondiffusive memory Comm. Partial Differential Equations , 35: (2): 245274 2010 ISSN: 03605302 DOI: 10.1080/03605300903473400[ 7] M. Escobedo, S. Mischler, J. J. L. Velázquez
On the fundamental solution of a linearized UehlingUhlenbeck equation Arch. Ration. Mech. Anal. , 186: (2): 309349 2007 ISSN: 00039527 DOI: 10.1007/s0020500700842[ 8] M. Escobedo, S. Mischler, J. J. L. Velázquez
Singular solutions for the UehlingUhlenbeck equation Proc. Roy. Soc. Edinburgh Sect. A , 138: (1): 67107 2008 ISSN: 03082105 DOI: 10.1017/S0308210506000655[ 9] Miguel Escobedo, J. J. L. Velázquez
On the fundamental solution of a linearized homogeneous coagulation equation Comm. Math. Phys. , 297: (3): 759816 2010 ISSN: 00103616 DOI: 10.1007/s002200101058z



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


2005  A. v. HumboldtJ. C. Mutis Research Award (Alexander von Humboldt Foundation) 


1999  Keynote speaker, Equadiff Congress, Berlin  2006  PDE session, International Congress of Mathematicians, Madrid, Spain  2007  Keynote speaker, Equadiff Congress, Vienna, Austria 


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


 Master theses: 1
 PhD theses: 4, currently 1


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