Welcome to the Claudio Muñoz's homepage
L.E. Dickson Instructor
Department of Mathematics
The University of Chicago
Office: Eckhart 330
(773)-702-5868
5734 S. University Avenue,
Chicago, Illinois 60637

email address
cmunoz at math dot uchicago dot edu
Teaching
Research Interests: Partial Differential Equations, in particular: soliton theory, collisions, integrability.
Publications
  1. Inelastic character of solitons of slowly varying gKdV equations, preprint, to appear in Comm. Math. Phys.
  2. Dynamics of soliton-like solutions for slowly varying, generalized gKdV equations: refraction vs. reflection, preprint, SIAM J. Math. Anal. Vol. 44 (2012), No. 1, pp. 1-60.
  3. (with M.A. Alejo and L. Vega) The Gardner equation and the L^2-stability of the N-soliton solution of the Korteweg-de Vries equation, preprint, to appear in Transactions of the AMS.
  4. On the soliton dynamics under slowly varying medium for NLS equations, preprint, to appear in Math. Annalen. doi: 10.1007/s00208-011-0706-8.
  5. Soliton dynamics for generalized gKdV equations in a slowly varying medium, preprint, Analysis and PDE Vol. 4 (2011), No. 4, 573-638. doi: 10.2140/apde.2011.4.573
  6. On the inelastic 2-soliton collision for generalized KdV equations, preprint, Int. Math. Res. Notices (2010) 2010 (9): 1624-1719.
  7. (with M. Clapp and M. Musso) Singular limits for the bi-laplacian operator with exponential non-linearity in $\mathbm R^4$, preprint, IHP Nonlinear Anal. vol. 25 (5) 2008, pp. 1015-1041.
  8. (with M. del Pino) The two-dimensional Lazer-McKenna conjecture for an exponential non-linearity, preprint, J. Diff. Eqns.  vol. 231 (1) 2006, pp. 108-134.
Preprints
  1. The Gardner equation and the stability of multi-kink solutions of the mKdV equation, preprint.
  2. Sharp inelastic character of slowly varying NLS solitons, preprint.
  3. On approximate controllability and stabilization of generalized KdV solitons, preprint.
Proceedings
  1. H^1-stability of mKdV multi-kinks, Journées EDP, June 2011, Biarritz, France.
  2. L^2-stability of multi-solitons, Séminaire X-EDP, Ecole Polytechnique, January 2011.
  3. Dynamics of soliton-like solutions for slowly varying, generalized KdV equations, Oberwolfach Report 2010.