JUAN CARLOS MUÑOZ  GRAJALES, PHD.

 

 

Professor at the Department of Mathematics,

Universidad del Valle, A. A. 25360, Cali, Colombia.

Facultad de Ciencias, Block 320, Office 3178.

 

Research Collaborator in the Fluid Dynamics Group

at the Instituto de Matemática Pura e Aplicada (IMPA), Brasil.

 

Phone and Fax:  (57-2) 3393227

mailto:jcarlmz@yahoo.com

 

 

 

FAVOR LLENAR LA ENCUESTA DE LOS CURSOS EN LA PAGINA WEB

http://evaluacioncursos.univalle.edu.co

 

 

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PUBLICATIONS

 

 

RESEARCH INTERESTS

 

FLUID MECHANICS :  We are interested in describing  solitary

wave scattering over an irregular section of a coast. The models

adopted are systems of hyperbolic or dispersive equations with

variable coefficients representing the inhomogeneous medium.

 

WAVE MOTION IN DISORDERED MEDIA :   Pulse shape stabilization

and time-reversal refocusing  (in transmittion and reflection) of

solitary waves in the presence of highly oscillatory topographies.

We also consider these phenomena for acoustic pulses propagating

through the earth croast.

 

 

NUMERICAL ANALYSIS :

 

Spectral and Lagrangian numerical methods for dispersive equations. Study of error, stability and convergence.

 

STUDY OF THE PROPERTIES OF SOLUTIONS FOR DISPERSIVE EQUATIONS :

Existence and uniqueness of solutions for Boussinesq type systems with

highly oscillatory coefficients and stability of solitary waves and Cnoidal waves for  generalized Benney-Luke equations. Models for internal waves. Decay of solutions of dispersive equations.

 

 

 

MATERIAL SOBRE ANÁLISIS FUNCIONAL

 

 

Espacios de Banach, espacios de Hilbert y Cálculo Diferencial:  Capítulo 2 del libro Manifolds, tensor analysis and applications, written by Ralph Abraham, Jerrod E. Marsden, Tudor S. Ratiu. Applied Mathematical Sciences 75, Springer, 2007).

 

 

Operadores no acotados

http://www.fismat.fisica.unlp.edu.ar/falomir/Notas-MF/No-acotados.pdf

(Notas del curso de Métodos de la Física Matemática, Análisis Funcional, H. Falomir, Departamento de Física, Facultad de Ciencias Exactas- UNLP).

 

 

SOFTWARE

 

Schwartz-Christoffel conformal mapping by T. Driscoll (For Matlab 6.0):

sct-ver5.zip (Zip file). This is a set of routines written for MATLAB which computes numerically

Schwartz-Christoffel type  transformations of domains with polygonal boundary.

 

 

PLANAR DOUBLE PENDULUM SIMULATION.

Download here executable penddoble.exe and data files phi.dat, theta.dat<<< NEW >>

Put these three files in the same directory.

 

 

 

SOME INTERESTING LINKS ON WAVES IN

DISORDERED MEDIA

(Time reversal refocusing and solitary wave scattering

in random media)

 

HOMEPAGES OF Knut Solna

R. Burridge, L. Berlyand

 

 

Time reversal mirror in the ocean: http://www.mpl.ucsd.edu/people/wak/

 

 

 

 

HOMEPAGES OF AUTHORS IN NUMERICAL METHODS

FOR PDEs

 

 

Uri Ascher

 

N. Trefethen

 

 

Spectral Methods and Fast Fourier Transform :

 

J. P. Boyd Chebyshev and Fourier Spectral Methods

 

Vozovoi, Israeli, Averbuch

 

 

 

LINKS ON TSUNAMIS : FORECASTING AND RESEARCH

 

http://www.geophys.washington.edu/tsunami/welcome.html