Volume 2, Number 1, Winter 1994
TRAVELLING FRONTS FOR
CORRELATED RANDOM WALKS
K.P. HADELER
Abstract. Scalar reaction diffusion equations describe
Brownian motion and multiplication of particles. These equations
are well understood, in particular, asymptotic behavior
of solutions and existence of travelling fronts. If Brownian
motion is replaced by a correlated random walk, then one
obtains nonlinear hyperbolic systems. The form of these system
depends essentially on the underlying assumptions. In
some cases these systems can be reduced to single hyperbolic
equations of which reaction diffusion equations appear as limit
cases. In other cases such reductions do not seem possible. In
the special case of one hyperbolic equation and in the general
case of a hyperbolic system the existence problem for travelling
front solutions is studied in detail.
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