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| This research is a natural continuation of our recent paper "Exact solutions
of the simplified Keller-Segel model" published in Commun Nonlinear Sci
Numer Simulat 2013; 18: 2960-2971. Here we show that the Keller-Segel
type system in the case of one space variable is linearisable. The linearization
procedure consists of a chain of substitutions, including the well-known Cole-
Hopf substitution. Moreover, using the classical results for the linear heat
equation and the Burgers equation, we construct exact solutions for the initial
problem and the boundary-value problem with the zero
fluxes in the case of
the Keller-Segel system in question. Uniqueness of the solutions obtained is
investigated and the relevant restrictions are derived. Finally, we present some
results, including Lie symmetry invariance and particular exact solutions, for
the model in the case of two space variables. |
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