Kolesov, A. Yu. A stability criterion of travelling waves for parabolic systems with small diffusion. (Russian) Zbl 0685.34059 Sib. Mat. Zh. 30, No. 3(175), 175-179 (1989). 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 Cited in 1 ReviewCited in 2 Documents MSC: 34D20 Stability of solutions to ordinary differential equations Keywords:orbital exponential stability; travelling waves PDFBibTeX XMLCite \textit{A. Yu. Kolesov}, Sib. Mat. Zh. 30, No. 3(175), 175--179 (1989; Zbl 0685.34059) Full Text: EuDML