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A stability criterion of travelling waves for parabolic systems with small diffusion. (Russian) Zbl 0685.34059

The author considers in \({\mathbb{R}}^ m\) the boundary value problem \[ \dot u=\epsilon Du''+F(u),\quad u|_{x=0}=u|_{x=2\pi};\quad u'|_{x=0}=u'|_{x=2\pi}, \] where \(D=diag(d_ 1,...,d_ m)\), \(d_ j>0\), \(j=1,...,m\), \(0<\epsilon \leq 1\) and F smooth and nonlinear. He proves that in some conditions the travelling waves of this problem are orbital exponential stable.
Reviewer: S.Balint

MSC:

34D20 Stability of solutions to ordinary differential equations
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