Welcome to Claudio Muñoz's homepage
Departamento de Ingeniería Matemática,
Facultad de Ciencias Físicas y Matemáticas,
Universidad de Chile
Beauchef 851, Torre Norte, Piso 5,
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
Martel (Video) and Frank Merle (Video 1,
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
EEQUADD MathAmSud Collaboration.
Well-posedness for modulationally unstable nonlinear Schrodinger equations, and
Nonexistence of small, odd breathers for a class of nonlinear wave
(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
(with Anna Kazeykina),
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
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),
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:
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.
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.
Dispersive PDEs (Spring 2016)
Multivariate Calculus (Spring 2016)
ODEs (Spring 2016)
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).