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Research topics

I work in the area of Applied Nonlinear Partial Differential Equations. My research interests include: Stability of Shock Profiles, Nonlinear Wave Propagation, Hydrodynamic Stability, Dynamics of Phase Transitions in Continuum Mechanics, and Mathematical Biology.

For a complete list of publications click here... »

Latest News:

January 1, 2024 | By: Ramón

• A new preprint on the stability of Néel walls in ferromagnetic thin films is available. This is a joint work with L. Morales (IIMAS, UNAM), A. Capella (IM, UNAM) and C. Melcher (RWTH, Aachen). The link to the preprint is here.

Current research topics

  1. Stability of shock profiles
    I study the asymptotic stability properties of shock profiles, namely, traveling wave solutions to different regularizations of hyperbolic systems of conservation laws, such as viscous, relaxation or radiative profiles, among others.
  2. Multidimensional stability of planar phase boundaries in continuum mechanics
    I have applied hyperbolic stability techniques to study the dynamics and stability of planar phase boundaries in continuum mechanics, such as planar interfaces between phases of nonlinear elastic materials, or planar boundaries between simple fluids. The techniques I use are based on the Kreiss-Majda-Métivier theory of stability of classical fronts.
  3. Existence and stability of nonlinear waves
    I study the general existence theory and stability properties of nonlinear waves, appearing in different circumstances. Among them you can find: traveling waves for coupled elasto-chemical models, solitons, periodic wavetrains, or diffusion fronts. 
  4. Mathematical Biology
    I work on chemotaxis and transport phenomena applied to biosciences. My work covers modelling, asymptotic analysis and numerical simulations.

Earlier work

  1. Pattern formation (morphogenesis)
    I have studied the effects of surface curvature and growth on pattern formation, by adapting the celebrated Turing mechanism of morphogenesis to time-dependent, curved domains.

Selected Talks

Here you can find a list of selected downloadable presentations:


Funding

My research has been partially supported by the following sources:

Current:

Research grants:

Other:


Past:

Research grants:

Other:


Research Visits

This is a list of recent academic departments I have visited:

  1. Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Universitá degli Studi dell'Aquila, Italia. September 11-15, 2023. Host: C. Lattanzio.
  2. Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Universitá degli Studi dell'Aquila, Italia. October 21 - December 21, 2017. Hosts: D. Donatelli, C. Lattanzio.
  3. Dipartimento di Matematica 'Guido Castelnuovo', University of Rome, La Sapienza, Rome, Italy. July 17 - 30, 2017. Host: C. Mascia.
  4. Department of Mathematics and Statistics. University of Sao Paulo, Brazil. October 1 - 20, 2015. Host: J. Angulo Pava.
  5. Department of Mathematical Sciences. University of Bath, UK. September 13 - 20, 2014. Host: A. Kyprianou.
  6. Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Universitá degli Studi dell'Aquila, Italia. November 5 - 30, 2013. Host: C. Lattanzio.
  7. Dipartimento di Matematica Pura ed Applicata, Universitá degli Studi dell'Aquila, Italia. September 20 - December 20, 2012. Host: C. Lattanzio.
  8. Department of Mathematics, Texas A&M University. April 2-7, 2012. Host: P. Howard.
  9. Dipartimento di Matematica Pura ed Applicata, Universitá degli Studi dell'Aquila, Italia. October 31 - November 5, 2011. Host: C. Simeoni.
  10. Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Spain. April 10-24, 2010. Hosts: G. Oleaga, J.J.L. Velázquez.
  11. Mathematics Institute, University of Leipzig, Germany. November 3-15, 2009. Hosts: W. König, S. Luckhaus.
  12. Department of Mathematics, Indiana University, Bloomington, U.S.A. April 5-18, 2009. Host: K. Zumbrun.
  13. Department of Mathematics, Indiana University, Bloomington, U.S.A. April 23 - May 4, 2008. Host: K. Zumbrun.
  14. Department of Mathematics, Indiana University, Bloomington, U.S.A. April 9-18, 2007. Host: K. Zumbrun.

Mentorship


Post-doctoral associates:

Theses under supervision:

Ph.D.

M.Sc.


Past students



Collaborators