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Finite dimensional dynamics for Kolmogorov-Petrovsky-Piskunov equation. (English) Zbl 1116.35064
The authors construct finite-dimensional submanifolds of the solution space for a reaction diffusion equation of Kolmogorov-Petrovsky-Piskunov type. In particular, the corresponding reduced evolutionary dynamics is described and exact solutions are found.

MSC:
35K57 Reaction-diffusion equations
35K55 Nonlinear parabolic equations
37L20 Symmetries of infinite-dimensional dissipative dynamical systems
37L05 General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations
35B42 Inertial manifolds
35B41 Attractors
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