Branching random motions, nonlinear hyperbolic systems and travelling waves Academic Article

abstract

  • A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independent of random motion, and intensities of reverses are defined by a particle's current direction. A solution of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) has a so-called McKean representation via such processes. Commonly this system possesses travelling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed. The paper realizes the McKean's program for the Kolmogorov- Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role. © EDP Sciences, SMAI 2006.

publication date

  • 2006/12/1

keywords

  • Branching
  • Convergence of Solutions
  • Feynman-Kac Formula
  • Hyperbolic Systems
  • Line
  • Motion
  • Nonlinear Equations
  • Nonlinear Hyperbolic Systems
  • Oliver Heaviside
  • Reverse
  • Traveling Wave
  • Traveling Wave Solutions

International Standard Serial Number (ISSN)

  • 1292-8100

number of pages

  • 22

start page

  • 236

end page

  • 257