Ítem
Acceso Abierto
Branching random motions, nonlinear hyperbolic systems and traveling waves
Título de la revista
Autores
Ratanov, Nikita
Archivos
Fecha
2004-07-07
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Editor
Editorial Universidad del Rosario
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Resumen
Abstract
A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A soluton of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) have a so-called McKean representation via such processes. Commonly this system possesses traveling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed.This Paper realizes the McKean programme for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.
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Keywords
Non-linear hyperbolic system , Branching random motion , Feynman-Kac connection , McKean solution , Traveling wave
