Research

Research in brief:

Nonlinear evolution partial differential equations. In particular, the study of front propagation phenomena in equations of pseudo-parabolic, kinetic,

parabolic and hyperbolic type. This amounts to study travelling waves and rarefaction waves, moving interfaces and fronts invading unstable states.

Some of my research on the above topics was motivated by physical problems arising in infiltration in porous media. Most recently,

I have looked at some fluid dynamic problems related to this issue from a more applied, although still mathematical, point of view. This includes

modelling and rigorous mathematical analysis of accumulation in thin-film viscous flows over a smooth substrate in a limit in which both gravity

and surface tension balance. Currently, I am also interested in understanding some processes of two-phase flow by stochastic analysis of simple models of

a two dimensional porous medium.

Some collaborators: M. Calle (formerly at Universidad Autónoma de Madrid), J.J.L. Velázquez (University of Bonn),

F. Achleitner and S. Hittmeir (Vienna University of Technology) and J.R. King (University of Nottingham).

PhD Students: 

J. Cayama (PhD 2020, supervised with F. de la Hoz) 

X.Diez (PhD 2021)

I. Girona (expected 2024, supervised with F. de la Hoz) 

L. Constantin (expected 2026, supervised with J. Giacomoni and G. Warnault, co-tutelle with Univ. Pau)

Research Projects:  

1. `Análisis Matemático y Numérico de Ecuaciones en Derivadas Parciales' PID2021-126813NB-I00, MICINN Sep'22 -Oct'25 (PIs: F. de la Hoz, L. Vega).

2. Grupo Consolidado: `Fourier Analysis and Partial Differential Equations'.  IT1615-22. GV. Jan'22 - Dic'25 (PI: C. Pérez).

Past projects:

3. 'Mathematical and Numerical Analysis of some Partial Differential Equations and its Applications' PGC2018-094522-B-I00, MICINN Jan'19-Oct'22. (PIs: C.Cuesta, L. Vega).

4.  Grupo Consolidado 'Fourier Analysis and Partial Differential Equations'  IT1247-19. GV Jan'19-Jan'22  (PI: C. Pérez).

5. 'Análisis Teórico y Numérico de Ecuaciones de Evolución' MTM2014-53145-P. MINECO, Jan'15-Jan'18. (PIs: L. Vega, C.Cuesta).

6.  Grupo consolidado `Mathematical Physics, Mathematical Analysis and Partial Differential Equations, and Numerical Analysis'. IT641-13, GV. Jan'13-Jan'19. (PI:L.Vega).

7.  'Proyecto de Excelencia Severo Ochoa' at ICMAT, SEV-2011-0087, MINECO (a member from Jan'12 to Ag'12, PI: M. de León).

8. 'Problemas matemáticos que surgen en fenómenos de propagación. MTM2011-24109. MICINN, Jan'12-Jan'15 (PI: C. Cuesta).

9. 'Propagation phenomena in nonlinear partial differential equations' RYC-2008-02127. Nov'09-Nov'11 (PI: C. Cuesta)

10. 'The role of regularisations in front propagation phenomena' EP/D06834/1. EPSRC, Nov'06-Nov'09 (PI: C. Cuesta).

11.  'Nonlinear Waves in Kinetic and Macroscopic Models II'. P18367. FWF, April'06-April'09 (PI: C. Schmeiser).

12. 'Nonlinear Waves in Kinetic and Macroscopic Models'. P16174. FWF, April'03-April'06 (PI: C.Schmeiser).

13. RTN HYKE (Hyperbolic and Kinetic Equations). UE “FP5 Human Potential” a member in April-July'03 .(PIs: several, G. Rein at Vienna).

14. RTN FRONTS-SINGULARITIES. UE “FP5 Human Potential” a member in several periods in 2002, 2003, 2005 and 2006 .(PIs: several, J. King at Notingham).

15. 'Dynamic Capillary Pressure in Porous Media'. REF: 620-61-386. NWO. PhD-project. Nov'97 (Supervisors: J. Hulshof and C.J. van Duijn)