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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:

December 3, 2015 | By: Ramón

• A new paper on the stability of traveling waves for Allen-Cahn models with relaxation, written in collaboration with C. Lattanzio, C. Mascia and C. Simeoni, has been accepted for publication in M3AS. Click here to access the preprint.
• Since January 2015, I am a member of the Editorial Board of Acta Applicandae Mathematicae.

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. In this area I collaborate with K. Zumbrun, T. Nguyen, C. Mascia, P. Howard, B. Kwon and C. Lattanzio.
  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. I collaborate with H. Freistühler and G. Lyng.
  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. I the study of such waves I collaborate with J. Angulo Pava, G. Flores, T. Nguyen, R. Marangell, C.K.R.T. Jones and P.D. Miller.
  4. Chemotaxis
    In collaboration with C. Simeoni, C. Mascia, A.A. Minzoni, C. Málaga and D. Pera, I work on chemotaxis and transport phenomena applied to biosciences. Our work covers modelling, asymptotic analysis and numerical simulations.


Earlier work

  1. Pattern formation (morphogenesis)
    In collaboration with P. Padilla, P. Maini, F. Sánchez and R. Barrio, 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. Department of Mathematics and Statistics. University of Sao Paulo, Brazil. October 1 - 20, 2015. Host: J. Angulo Pava.
  2. Department of Mathematical Sciences. University of Bath, UK. September 13 - 20, 2014. Host: A. Kyprianou.
  3. Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Universitá degli Studi dell'Aquila, Italia. November 5 - 30, 2013. Host: C. Lattanzio.
  4. Dipartimento di Matematica Pura ed Applicata, Universitá degli Studi dell'Aquila, Italia. September 20 - December 20, 2012. Host: C. Lattanzio.
  5. Department of Mathematics, Texas A&M University. April 2-7, 2012. Host: P. Howard.
  6. Dipartimento di Matematica Pura ed Applicata, Universitá degli Studi dell'Aquila, Italia. October 31 - November 5, 2011. Host: C. Simeoni.
  7. Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Spain. April 10-24, 2010. Hosts: G. Oleaga, J.J.L. Velázquez.
  8. Mathematics Institute, University of Leipzig, Germany. November 3-15, 2009. Hosts: W. König, S. Luckhaus.
  9. Department of Mathematics, Indiana University, Bloomington, U.S.A. April 5-18, 2009. Host: K. Zumbrun.
  10. Department of Mathematics, Indiana University, Bloomington, U.S.A. April 23 - May 4, 2008. Host: K. Zumbrun.
  11. Department of Mathematics, Indiana University, Bloomington, U.S.A. April 9-18, 2007. Host: K. Zumbrun.


Students

Ph.D.

M.Sc.

B.Sc.

Past students


Collaborators