Welcome to Claudio Muñoz's homepage

Chargé de Recherche CNRS and Departamento de Ingeniería Matemática, Universidad de Chile
Director of Doctoral studies at DIM
cmunoz@dim.uchile.cl


Postal Address:
Departamento de Ingeniería Matemática,
Facultad de Ciencias Físicas y Matemáticas,
Universidad de Chile
Beauchef 851, Torre Norte, Piso 5,
Santiago, Chile
Phone: (+56)(2) 2978 0737

Research interests: Nonlinear dispersive equations, in particular: collisions, well-posedness, stability and asymptotic stability and blow-up.

I obtained a Ph.D. in Mathematics at the University of Versailles Saint-Quentin, under the advise of Yvan Martel (Video) and Frank Merle (Video 1, Video 2).

2nd. Workshop on Nonlinear Evolution Equations in Valdivia, to be held at Universidad Austral de Chile, Valdivia, on December 12-16 2016.
Partially funded by ERC Blowdisol, CAPDE Nucleo Milenio, CMM and EEQUADD MathAmSud Collaboration.


Recent preprints:

Well-posedness for modulationally unstable nonlinear Schrodinger equations, and applications, arXiv:1608.08169.
Nonexistence of small, odd breathers for a class of nonlinear wave equations, (with M. Kowalczyk and Y. Martel), arXiv:1607.06421, accepted in Letters Math. Phys.
Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II. (with Anna Kazeykina), arXiv:1603.06600.
Kink dynamics in the phi^4 model: asymptotic stability for odd perturbations in the energy space (with M. Kowalczyk and Y. Martel), arXiv:1506.07420, accepted in JAMS.
Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation (with Anna Kazeykina), arXiv:1502.00968, J. Funct. Anal. 270 (2016), no. 5, 1744-1791.
Asymptotic Stability of high-dimensional Zakharov-Kuznetsov solitons (with R. Cote, D. Pilod, and G. Simpson), arXiv:1406.3196, Arch. Rat. Mech. Anal. 220 (2016), no. 2, 639–710.
On the Variational Structure of Breather Solutions (new and expanded version, with M.A. Alejo and J.M. Palacios), arXiv:1309.0625.
Dynamics of complex-valued modified KdV solitons with applications to the stability of breathers (with M.A. Alejo), arXiv:1308.0998, Anal. and PDE. 8 (2015), no. 3, 629–674.

All my papers are in the ArXiv, and Mathscinet, done in collaboration with several kind researchers.
My research is partially supported by Fondecyt Regular No. 1150202, Center for Mathematical Modelling (CMM), and Nucleus Millenium Center CAPDE.

Some videos about soliton dynamics: KdV Video 1, quartic KdV Video 2 and the wobbling kink of Sine-Gordon Video 3. A periodic mKdV breather with nonzero mean: Video 1, Video 2, and Video 3.


Projects:

I'm an associate researcher in the CAPDE collaboration, lead by Manuel del Pino. We run a biweekly seminar: CAPDE Seminar 2015
I was also organizer of the PDE session at Somachi 2015.
I'm also part of the organizing comitee at CLAM 2016 Nonlinear dispersive equations session, taking place in Colombia between July 11-15 2016.
I'm also part of the MathAmSud collaboration EEQUADD 2016-2017.


Teaching:

Current teaching:

Dispersive PDEs (Spring 2016)
Multivariate Calculus (Spring 2016)
ODEs (Spring 2016)

Past teaching:

Advanced PDEs (Spring 2015) (Main documents, in Spanish: Midterm 1, Midterm 2, Final Exam, some additional lecture notes).
Multivariate Calculus (Fall 2015).

At the University of Chicago (2011-2013):
Multivariate Calculus II,
Introduction to Complex Analysis,
Honors Calculus I-II-III, and
Mathematical Methods for Physics.

At the University of Chile:
Ordinary Differential Equations (2011).