Mosaico Alhambra

Research



Research topics

  • Nonlinear Spreading PDE: Flux limitation, flux-saturation, Porous media equations, Waiting time, Pattern formation, Traveling waves, Discontinuous Waves, Optimal mass transportation, Entropy solutions, Relativistic heat equation.
  • Kinetic Theory and Conservations Laws: Hydrodynamical Limits, Gravitation, Relativity, Fragmentation-Coagulation, Vlasov, Boltzmann, BGK. Aplications: Social Systems, Traffic, Multicellular Systems.
  • Fluid Mechanics: Euler, Navier-Stokes, Singular solutions, Vortex Methods, Thin Films.Fluid Mechanics: Euler, Navier-Stokes, Singular solutions, Vortex Methods, Thin Films.
  • Developmental Biology. Mathematical Biology: Morphogenetic gradients, Hedgehog, Chemotaxis, Multicellular Interaction Systems, DNA Models, Flux-limited, Flux-saturated, Filopodia-like structures, Citonemes, Pattern formation, Traveling waves.
  • Quantum Mechanics: Semiconductors, Schrödinger, Wigner, Boltzman, Drift-diffusion.

Recent PhD Students

  • David Poyato. Since 2015 he is doing his doctoral thesis in the framework of a Spanish grant FPU.

Former PhD Students

  • José Antonio Carrillo defended his PhD. Thesis "Study of weak solutions of the Vlasov-Poisson-Fokker-Planck equations" in 1996. He is currently Professor at Imperial College (London), Chair in Applied and Numerical Analysis. In Spain, he is University Professor (Catedrático acreditado) and assigned to ICREA (Catalunya), researcher on leave. Upon completion of his thesis he conducted a 2-year postdoctoral fellowship at the University of Texas at Austin under the supervision of Irene Gamba.

  • José Luis López defended his PhD. Thesis "Analysis of partial differential equations in kinetic and quantum theory" in 1999. He is currently Associate Professor (Profesor Titular de Universidad) at University of Granada. During the completion of his thesis and later, he made pre and post-doctoral long-term research stays at University Paul Sabatier (Toulouse) under the supervision of Pierre Degond.

  • Juan José Nieto defended his PhD. Thesis "Asymptotic methods in partial differential equations arising in kinetics and quantum theory" in 2001. He is currently Associate Professor (Profesor Titular de Universidad) at University of Granada. During the completion of his thesis and later, he made pre and post-doctoral long-term research stays (over 2 years) at University Sophia Antipolis (Nice) under the supervision of Frédéric Poupaud. He obtained a post-doctoral position at  University Carlos III (Madrid).

  • Óscar Sánchez defended his PhD. Thesis "Deterministic and stochastic PDE arising in semiconductor theory and stellar dynamics" in 2003. He is currently Associate Professor (Profesor Titular de Universidad) at University of Granada. Previously he won a contract of Assistant Professor at University Carlos III (Madrid). He made a post-doctoral long-term research stay in CEREMADE (Paris-Dauphine) under the supervision of Jean Dolbeault. Later, he was hired as a Visiting Professor in CEREMADE.

  • José Alfredo Cañizo defended his PhD. Thesis "Some problems related to the study of interaction kernels: Coagulation, fragmentation and diffusion in kinetic and quantum equations" in 2006. He has currently a “Ramón y Cajal” contract at University of Granada. He was Lecturer at the University of Birmingham until the end of 2014. Previously, he was a post-doctoral fellow “Juan de la Cierva” at Universitat Autónoma of Barcelona under the supervision of J. A. Carrillo, and held a pre-doctoral stay at University of Berkeley. After completing his thesis, he carried out a post-doctoral stay of two years in CEREMADE (Paris-Dauphine) under the supervision of Stéphane Mischler.

  • Juan Calvo defended his PhD. Thesis "Dispersion vs. diffusion in transport PDE equations" in 2010, of which O. Sanchez was the co-advisor. He has currently a post-doctoral “La Caixa” contract at Centre de Recherca Matematica (CRM) in Barcelona under the supervision of Tomás Alarcón. He was a postdoctoral fellow “Juan de la Cierva” at University Pompeu Fabra under the supervision of Vicent Caselles. Previously, he enjoyed a post-doctoral fellowship at University of Granada and performed long-term research stays at Brown (with Yan Guo), Pavia (with Matteo Novaga), Paris VI (with Marie Doumic) and Maryland (with Pierre Emmanuel Jabin).

  • Pilar Guerrero defended her PhD. Thesis "Analysis of dissipation and diffusion mechanisms modeled by nonlinear PDEs in developmental biology and quantum mechanics" in 2010, of which J. L. López was the co-advisor. She is currently Postdoctoral Research Associate in Mathematical Biology at University College of London, and collaborates with the teams of Dr. Karen Page (UCL Mathematics) and Dr. James Briscoe (National Institute of Medical Research, Developmental Neurobiology). Previously, he obtained a two-years post-doctoral contract at Centre de Recherca Matematica (CRM) in Barcelona under the supervision of Tomás Alarcón.

  • María Ofelia Vásquez defended her PhD. Thesis "Partial differential equations for the analysis of biopolymeric models" in 2015, of which J. Nieto was the co-advisor. She is currently Assistant Professor at University of Cartagena (Colombia).

Editorial boards

  • Mathematical Models and Methods in the Applied Sciences
  • EMS Surveys in Mathematical Sciences
  • AMS-RSME book series: Mathematical Surveys and Monographs, University Lecture Series, Graduate Studies in Mathematics.


Grants

For a more comprehensive list of projects, we refer the reader to the web site of the research group 'Partial Differential Equations in Kinetic Theory' or in the item 'Previous grants' below. We cite here those who are currently active.

  • Dinámica evolutiva, teoría cinética y descripciones hidrodinámicas en ciencias de la vida: MTM2014-53406-R
    Sponsor: MINECO: Ministerio de Economía y Competitividad (Proyectos de I+D+I: Retos de investigación)
    Members: Universidad de Granada
    Period: from 01/01/15 to 31/12/18
    PI: Juan Soler
  • Modelado matemático de sistemas complejos en Ciencias de la Vida: de la dinámica tumoral al comportamiento colectivo de especies (BIOMAT): FQM-954
    Sponsor: Junta de Andalucía (Proyecto de excelencia)
    Members: Universidad de Granada
    Period: from 01/01/14 to 31/12/17
    PI: Juan Soler
  • Ecuaciones de Evolución en Derivadas Parciales. FQM316
    Sponsor: Junta de Andalucía
    Members: Universidad de Granada
    Period: from 01/05/01 to: (open)
    PI: Juan Soler

Previous grants.

  • Ecuaciones de evolución para sistemas complejos en ciencias de la vida y teoría cinética: MTM2011-23384
    Sponsor: Ministerio de Ciencia e Innovación / FEDER
    Members: Universidad de Granada
    Period: from 01/01/12 to 31/12/14
    PI: Juan Soler
  • BIOMAT: Modelos matemáticos en vías de señalización originados en dinámica tumoral, sistemas complejos multicelulares, neurociencia y coagulación sanguínea: FQM-4267
    Sponsor: Junta de Andalucía (Proyecto de excelencia)
    Members: Universidad de Granada
    Period: from 13/01/09 to 12/01/12
    PI: Juan Soler
  • Modelización y análisis matemático de fenómenos no lineales en teoría cinética de EDPs con origen en biomedicina (dinámica tumoral y vías de señalización) y astrofísica: MTM2008-05271
    Sponsor: Ministerio de Ciencia e Innovación
    Members: Universidad de Granada
    Period: from 01/01/09 to 31/12/11
    PI: Juan Soler
  • Modélisation Analyse Simulation d'Ondes Hydrodynamiques
    Sponsor: INRIA (Projet Méditerranée 3+3)
    Members: 5 nodos (Francia, Marruecos, Túnez y España-UGR) 
    Period: from 16/06/06 to 15/06/09
    PI: Thierry Goudon (Juan Soler del nodo español)
  • Biomat: estudio de modelos de desarrollo y movilidad celular y tumoral: FQM-1268
    Sponsor: Junta de Andalucía (Proyecto de excelencia)
    Members: Universidad de Granada
    Period: from 01/01/06 to 31/12/2008
    PI: Juan Soler
  • Estabilidad y Efectos Dispersivos de EDPs en Mecánica Cuántica/de Fluidos y Problemas Cinéticos de Radiación: MTM2005-02446
    Sponsor: Ministerio de Eduación y Ciencia
    Members: Universidad de Granada
    Period: from 31/12/05 to 30/12/08
    PI: Juan Soler
  • Ecuaciones deterministas y estocásticas en derivadas parciales en teoría de transporte cinético y cuántico: BFM2002-00831
    Sponsor: Ministerio de Ciencia y Tecnología
    Members: Universidad de Granada
    Period: from 01/10/02 to 30/09/05
    PI: Juan Soler
  • Hyperbolic and Kinetic Equations: Asymptotics, Numerics, Applications. HPRN-CT-2002-00282 
    Sponsor: European Union
    Members: 15 european teams
    Period: from 01/06/02 to 31/05/05
    PI: Juan Soler (Team organizer of E2-Granada)
  • Acción Integrada Hispano-Francesa: Modelos en E.D.P. para Semiconductores y Transiciones de Fase: HF2002-0084
    Sponsor: Ministerio de Ciencia y Tecnología
    Members: Universidad de Granada, Université de Nice, Université de Paris VI
    Period: from 01/01/03 to 31/12/04
    PI: Juan Soler (Universidad de Granada), Frédéric Poupaud (Université de Nice)
  • Ecuaciones en Derivadas Parciales originadas en Teoría Cinética y Cuántica. PB98-1281
    Sponsor: Ministerio de Ciencia y Tecnología
    Entidades participantes: Universidad de Granada, Université de Nice, Wien University
    Period: from 01/12/99 to 01/12/02
    PI: Juan Soler
  • Asymptotic Methods in Kinetic Theory. TMR ERB FMBX-CT97-0157
    Sponsor:European Union
    Members:8 european teams
    Period: from 01/04/98 to 31/12/01
    PI: Juan Soler (Granada team)
  • Acción Integrada Hispano-Austriaca: Estudio de modelos disipativos en transporte cinético-cuántico en física de semiconductores y Astrofísica: MCYT HU99-0033
    Sponsor: Ministerio de Ciencia y Tecnología
    Members:Universidad de Granada, Wien University
    Period: from 01/01/00 to 31/12/01
    PI: Juan Soler (Spanish team), Peter Markowich (Austrian team)
  • Unidad Especializada de la Junta de Andalucía de los grupos de investigadores principales: F. Águila, E. Battaner, R. Ortega, R. Payá y J. Soler
    Sponsor: Junta de Andalucía
    Members: Universidad de Granada
    Period: from 01/05/01 to 31/05/02 
    PI: Juan Soler
  • Acción Integrada Hispano-Alemana: Comportamiento asintótico de ecuaciones parabólicas y sistemas de Schrödinger
    Sponsor: Ministerio de Educación y Ciencia
    Members:Universidad de Granada, Universität des Saarlandes
    Period: from 01/01/99 to: 31/12/00 
    PI: Juan Soler (Spanish team), Anton Arnold (German team)
  • Acción Integrada Hispano-Italiana: Métodos asintóticos para el estudio de EDP originados en teoría cinética, cinetico-cuántica y mecánica de fluidos.
    Sponsor: Ministerio de Educación y Ciencia
    Members: Universidad de Granada, Università degli Studi di Roma "La Sapienza"
    Period: from 01/01/98 to 31/12/99 
    PI: Juan Soler (Spanish team), Mario Pulvirenti (Italian team)
  • Acción Integrada Hispano-Alemana: El sistema de Wigner-Poisson-Fokker-Planck y cambios de escala en transporte cuántico de partículas
    Sponsor: Ministerio de Educación y Ciencia
    Members: Universidad de Granada, Technishe Universität Berlin
    Period: from 01/01/97 to 31/12/98 
    PI: Juan Soler (Spanish team), Peter Markowich (German team)

 


Colaborations