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| 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 |
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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]).
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[ 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 |
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| 2005 | A. v. Humboldt-J. C. Mutis Research Award. (Alexander von Humboldt Foundation) |
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| 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. |
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SIAM J. Math. Analysis (2001--2005); Rev. Math. Iberoamericana (2001--2008).
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Responsible of two grants of the Spanish Government about "Partial Differential Equations in Mathematical Physics", during the periods 2004--2007 and 2007--2010.
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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. |
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Marco A. Fontelos (1997), now Universidad Autonoma de Madrid; Gerardo Oleaga (2000), now Universidad Complutense Madrid.
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- Master theses: 1
- PhD theses: 4, currently 1
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