Profile
Profile

Prof. Dr. Juan J. L. Velázquez

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

Academic Career

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

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 (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]).

Research Projects and Activities

Responsible of two grants of the Spanish Government about “Partial Differential Equations in Mathematical Physics”
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 models 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 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

Publication List

Editorships

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

Awards

2005

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

Selected Invited Lectures

1999

Keynote speaker, Equadiff Congress, Berlin

2006

PDE session, International Congress of Mathematicians, Madrid, Spain

2007

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

Supervised Theses

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