JUAN CARLOS MUÑOZ GRAJALES
Research
My research areas include:
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 transmission and reflection) of solitary waves in the presence of highly oscillatory topographies. We also consider these phenomena for acoustic pulses propagating through the earth crust.
NUMERICAL ANALYSIS :
Spectral and Lagrangian numerical methods for dispersive equations. Study of error, stability and convergence. Finite element methods applied to dispersive evolution equations.
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.
INVERSE PROBLEMS FOR PARTIAL DIFFERENTIAL EQUATIONS (PDEs):
Analytical and numerical study of inverse problems associated to initial-boundary value problems for Partial Differential Equations: coefficient identification.