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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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