**Welcome to Claudio Muñoz's homepage**

**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).

**Workshop
MathAmSud EEQUADD**,
to be held at Universidad de Chile, Santiago, on December 4-7 2017.

Partially funded by CAPDE Nucleo Milenio, CMM and EEQUADD MathAmSud Collaboration.

**
Publications and preprints:
**

*Breathers and the dynamics of solutions to the KdV type equations * (with G. Ponce), preprint arXiv:1803.05475 (improvement of a previous paper arXiv:1802.05547)

*Extended decay estimates for generalized BBM equations* (with C. Kwak), preprint arXiv:1802.01925

*Nonlinear stability of 2-solitons of the Sine-Gordon equation in the energy space* (with J. M.
Palacios), preprint arXiv:1801.09933

*The scattering problem for the abcd Boussinesq system in the energy
space* (with C. Kwak, F. Poblete and J. C. Pozo), preprint arXiv:1712.09256

*On asymptotic stability of nonlinear waves,
* (with M. Kowalczyk and Y. Martel), Laurent Schwartz
seminar notes 2016-2017.

*
Scattering in the energy space for Boussinesq equations,
* (with F. Poblete and J.C. Pozo), preprint arXiv:1707.02616, to appear in Comm. Math. Phys.

*
Almost sharp nonlinear scattering in one-dimensional Born-Infeld equations arising in
nonlinear Electrodynamics,
* (with M.A. Alejo), preprint arXiv:1707.02595. Accepted in PAMS.

*
Stability of KdV solitons on the half-line,
* (with Marcio Cavalcante), preprint arXiv:1707.02608.

*Instability in nonlinear Schrodinger breathers*, arXiv:1608.08169, Proyecciones
Vol. 36, no. 4 (2017) 653--683.

*Nonexistence of small, odd breathers for a class of nonlinear wave
equations*,
(with M. Kowalczyk and Y. Martel), arXiv:1607.06421, in L. Math. Phys. May 2017,
Vol. 107, Issue 5, pp. 921-931.

*
Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV
equation. II.
*
(with Anna Kazeykina),
arXiv:1603.06600, to appear in J. Diff. Eqns.

*
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 30 (2017), 769-798.

*
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 I* (with M.A.
Alejo and J.M. Palacios),
arXiv:1309.0625
accepted in JMAA Vol. 453 2, 1111-1138.

*
On the Variational Structure of Breather Solutions II* (with M.A.
Alejo and J.M. Palacios),
arXiv:1309.0625, accepted in EJDE Vol. 2017 (2017), No. 56,
pp. 1-26.

*
The Gardner equation and the stability of multi-kink solutions of the mKdV equation,
*
arXiv:1106.0648, Discrete and Continuos Dynamical
Systems 36 (7), 3811-3843.

*
Stability of integrable and nonintegrable structures,
* arXiv:1510.03366, Advances in Differential
Equations 19 (9/10), 947-996.

*
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.

*
On approximate controllability and stabilization of generalized KdV solitons,
* arXiv:1206.2430, SIAM Journal on Control and
Optimization 52 (1), 52-81.

*
Multi-solitons for nonlinear Klein-Gordon equations,
* arXiv:1210.7953, (with Raphael Cote), Forum of
Mathematics, Sigma 2.

*
Nonlinear stability of mKdV breathers
* (with M.A. Alejo), arXiv:1206.3157, Communications
in Mathematical Physics 324 (1), 233-262.

*
On nonlinear stability of mKdV breathers
* (with M.A. Alejo), arXiv:1206.3151, in J. Phys.
A: Math. Theor. Vol 45, no. 43.

*
Dynamics of soliton-like solutions for slowly varying, generalized gKdV equations: refraction vs.
reflection,
* arXiv:1009.4905, SIAM Journal on Mathematical
Analysis 44 (1), 1-60.

*
Sharp inelastic character of slowly varying NLS solitons,
* preprint arXiv:1202.5807.

*
The Gardner equation and the L^2-stability of the N-soliton solution of the Korteweg-de Vries
equation
* (with M.A. Alejo and L. Vega), arXiv:1012.5290, T.
of the AMS 365 (1),
195-212.

*
Inelastic character of solitons of slowly varying gKdV equations,
* arXiv:1107.5328, Communications in Mathematical
Physics 314 (3), 817-852.

*
On the soliton dynamics under slowly varying medium for NLS equations,
* arXiv:1002.1295, Mathematische Annalen 353 (3),
867-943.

*
On the inelastic 2-soliton collision for generalized KdV equations,
* arXiv:0903.1240, IMRN 2010 (9), 1624-1719.

*
Soliton dynamics for generalized gKdV equations in a slowly varying medium,
* arXiv:0912.4725, Analysis & PDE 4 (4), 573-638.

*
Singular limits for the bi-laplacian operator with exponential non-linearity in R^4
* (with M. Musso and M. Clapp), arXiv:0709.2878, Annales de l'IHP Non Linear Analysis 25
(5), 1015-1041.

*
The two-dimensional Lazer-McKenna conjecture for an exponential non-linearity,
* (with M. del Pino), arXiv:math/0608168, Journal
of
Differential equations 231 (1), 108-134.

*
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 2017
*

I was also part of the organizing committee of the 2nd. Workshop on Nonlinear
Evolution Equations in
Valdivia, 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.

I was also organizer of the PDE session
at Somachi 2015.

I was 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:
*

Multivariate Calculus (Fall 2017),

Advances dispersive PDEs (Fall 2017).

*
Past teaching:
*

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).