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.
- Alexis Béjar-López. Since 2020 he is doing his doctoral thesis in the framework of a Spanish grant FPU (coadvisor Pierre-Emmanuel Jabin).
- Carlos Pulido. Since 2020 he is doing his doctoral thesis in the framework of a Spanish grant FPI (coadvisor Juan Campos).
- Elena Torres. Since 2021 she is doing her doctoral thesis in the framework of a Spanish grant FPU.
- 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 the University of Oxford. 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. He has been Professor at Imperial College (London).
- 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 is currently Associate Professor (Profesor Titular de Universidad) at University of Granada, previously he had 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).
- David Poyato defended his PhD. Thesis "Macroscopic Limits, Self-Organization and Stability in Systems with Singular Interactions Arising from Hydrodynamics and Life Sciences" in 2019. Since November 2019, He is a postdoc researcher at Institut Camille Jordan (Université Claude Bernard Lyon 1) associated to the ERC grant MESOPROBIO leaded by Prof. Vincent Calvez.
- Claudia García defended her PhD. Thesis "Patterns in Partial Differential Equations Arising from Fluid Mechanics
" in 2020. Co-advisor Taoufik Hmidi (Univerty of Rennes). She has a postdoctoral position at the University of Granada until February 2021, and since February 2021 she will be a postdoc researcher at University of Barcelona associated to the ERC Starting Grant 852741 leaded by Prof. Javier Gómez-Serrano.
- Cleyton Cunha defended his PhD. Thesis "Some contributions to the study of incompressible micropolar fluids in two dimensional domains
" in 2020 at the Universidade Federal de Pernambuco (Brazil). Co-advisor Pablo Braz e Silva (Universidade Federal de Pernambuco). He has an associate professor position at the Universidade Federal do Delta do Parnaíba - UFDPar (Brazil).
- Martina Conte defended her PhD. Thesis "Mathematical models for glioma growth and migration inside the brain
" in 2021 at the at Basque Center for Applied Mathematics / Basque Country University. Co-advisor Luca Gerardo-Giorda (Johannes Kepler University and RICAM, Linz). She has a postdoctoral position at the Politecnico di Torino.
- Mathematical Models and Methods in the Applied Sciences
- EMS Surveys in Mathematical Sciences
- AIMS Biophysics
- 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.
- PADY (Pattern Dynamics in Nonlinear Partial Differential Equations arising in Fluid and Cell Mechanics) Dinámica de patrones en EDPs no lineales originadas en mecánica celular y de fluidos: RTI2018-098850-B-I00
Sponsor: MICINN, Proyectos de I+D "Retos investigación"
Members: Universidad de Granada
Period: from 01/01/19 to 31/12/23
PI: Juan Soler y Juan Campos
- GLIOMAT: Modelos matemáticos en comunicación celular mediada por citonemas y dinámica de glioblastomas: P18-RT-2422
Sponsor: Junta de Andalucía, PAIDI - Modalidad "Retos Consolidado"
Members: Universidad de Granada
Period: from 01/01/20 to 31/12/22
PI: Juan Soler y Juanjo Nieto
- NL-DISCOM: Dispersión no lineal, comunicación celular y dinámica tumoral : A-FQM-311-UGR18
Sponsor: Junta de Andalucía, Prog. Operat. FEDER Andalucía - Modalidad "Frontera"
Members: Universidad de Granada
Period: from 01/01/19 to 30/06/21
PI: Juan Soler y Juan Calvo
- 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)
