Profile
Profile

Prof. Dr. Juan J. L. Velázquez

E-mail: velazquez(at)iam.uni-bonn.de
Phone: +49 228 73 62378
Room: 2.023
Location: Mathematics Center
Institute: Institute for Applied Mathematics
Research Area: Research Area B
Birthdate: 27.Jun 1964
Mathscinet-Number: 289301

Publications

Academic Career

1990

Ph D, Mathematics, Universidad Complutense, Madrid

1991--1992

Postdoctoral stay, IMA, University of Minnesota

1992--1997

Associate Professor at the Applied Mathematics Department, Universidad Complutense, Madrid

1997--2008

Full Professor at the Applied Mathematics Department, Universidad Complutense, Madrid

2008--2011

Research Professor at Institute de Ciencias Matematicas, CSIC, Madrid

2011--

Full Professor (W3), Bonn

Research profile

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 ([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]).

Selected Publications

[1] Miguel A. Herrero, Juan J. L. Velázquez
Singularity patterns in a chemotaxis model
Math. Ann. , 306: (3): 583--623
1996
ISSN: 0025-5831
DOI: 10.1007/BF01445268
[2] J. J. L. Velázquez
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 (electronic)
2004
ISSN: 0036-1399
DOI: 10.1137/S0036139903433888
[3] Elio Eduardo Espejo Arenas, Angela Stevens, Juan J. L. Velázquez
Simultaneous finite time blow-up in a two-species model for chemotaxis
Analysis (Munich) , 29: (3): 317--338
2009
ISSN: 0174-4747
DOI: 10.1524/anly.2009.1029
[4] A. Stevens, J. J. L. Velázquez
Partial differential equations and non-diffusive structures
Nonlinearity , 21: (12): T283--T289
2008
ISSN: 0951-7715
DOI: 10.1088/0951-7715/21/12/T04
[5] Kyungkeun Kang, Benoit Perthame, Angela Stevens, J. J. L. Velázquez
An integro-differential equation model for alignment and orientational aggregation
J. Differential Equations , 246: (4): 1387--1421
2009
ISSN: 0022-0396
DOI: 10.1016/j.jde.2008.11.006
[6] Kyungkeun Kang, Angela Stevens, Juan J. L. Velázquez
Qualitative behavior of a Keller-Segel model with non-diffusive memory
Comm. Partial Differential Equations , 35: (2): 245--274
2010
ISSN: 0360-5302
DOI: 10.1080/03605300903473400
[7] M. Escobedo, S. Mischler, J. J. L. Velázquez
On the fundamental solution of a linearized Uehling-Uhlenbeck equation
Arch. Ration. Mech. Anal. , 186: (2): 309--349
2007
ISSN: 0003-9527
DOI: 10.1007/s00205-007-0084-2
[8] M. Escobedo, S. Mischler, J. J. L. Velázquez
Singular solutions for the Uehling-Uhlenbeck equation
Proc. Roy. Soc. Edinburgh Sect. A , 138: (1): 67--107
2008
ISSN: 0308-2105
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): 759--816
2010
ISSN: 0010-3616
DOI: 10.1007/s00220-010-1058-z
[10] Miguel A. Herrero, Juan J. L. Velázquez
A blow-up mechanism for a chemotaxis model
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , 24: (4): 633--683 (1998)
1997
ISSN: 0391-173X
File: http://http://www.numdam.org/item?id=ASNSP_1997_4_24_4_633_0

Awards

2005

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

Invited Lectures

1999

Keynote speaker in the Equadiff Congress, Berlin.

2006

PDE session of the International Congress of Mathematicians (Madrid ).

2007

Keynote speaker in the Equadiff Congress, Vienna.

Editorships

SIAM J. Math. Analysis (2001--2005); Rev. Math. Iberoamericana (2001--2008).

Research Projects and Activities

Responsible of two grants of the Spanish Government about "Partial Differential Equations in Mathematical Physics", during the periods 2004--2007 and 2007--2010.

Contribution to Research Areas

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 modelsm as well as kinetic models with fluxes of particles between different regions of the phase space. Well-posedness 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.

Selected PhD students

Marco A. Fontelos (1997), now Universidad Autonoma de Madrid; Gerardo Oleaga (2000), now Universidad Complutense Madrid.

Supervised Theses

  • Master theses: 1
  • PhD theses: 4, currently 1
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