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Construction of the rotation of a vector field for operators describing wave solutions of parabolic systems. (English. Russian original) Zbl 0704.35067
Sov. Math., Dokl. 36, No. 3, 452-455 (1988); translation from Dokl. Akad. Nauk SSSR 297, 280-283 (1987).
The authors show that the rotation of the vector field for operators describing the traveling wave solutions \(u(x,t)=w(x-ct)\) of parabolic systems \(\partial u/\partial t=a\partial^ 2u/\partial x^ 2+F(u)\) can be constructed under an appropriate choice of spaces. Here a is a symmetric, positive-definite, square matrix of order n, \(u=(u_ 1,...,u_ n)\), \(F=(F_ 1,...,F_ n)\), \(x\in {\mathbb{R}}^ 1\) and \(t>0\).
Reviewer: T.A.Dzhangveladze

35K55 Nonlinear parabolic equations
35B99 Qualitative properties of solutions to partial differential equations