Multistability in nonlinear parabolic systems with low diffusion

Kashchenko, I. S.
December 2010
Doklady Mathematics;Dec2010, Vol. 82 Issue 3, p878
Academic Journal
The article studies the local dynamics of the system of nonlinear parabolic-type equations in the case where the matrices have no eigenvalues in the right complex half plane. It considers the systems of nonlinear parabolic-type equations with periodic boundary equations. It notes that known methods to study nonlinear dynamics based on the methods of local integral invariant manifolds and normal forms does not apply on the equations. It mentions that a method in studying the local dynamics has been developed which makes it possible in constructing special evolution equations.


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