Seminario

Seminario Análisis y EDPs

OPENING OF THE ANALYSIS & PDEs SEMINAR: Solutions of delay differential equations, including applications to electrodynamics.

Ponente:  Rafael de la Llave (Georgia Tech)
Fecha:  miércoles 29 de septiembre de 2021 - 15:00
Lugar:  Online - us06web.zoom.us/j/81491079139?pwd=OWo1TWc0NEExNDJZUFljWVRIdkZRQT09 (ID: 814 9107 9139; Access code: 937701)

Resumen:

The study of electrodynamics and other applied problems leads to the study of equations in which the forces are functions of the trajectory at previous times.  These delays depend on the trajectory. 

For such equations, not even the appropriate phase space is known. Much less a theory of existence and smoothness of  evolution.  

We show that, nevertheless,  there is a systematic theory to construct  many solutions. In particular
we  develop a theory of perturbations for small delays (the 1/c expansions in classical electrodynamics).  The theory is efective and leads to constructive numerical 
algorithms. 

This is based on joint works with J.Gimeno, X. He, J. Yang. and A. Casal, L. Corsi.