Babin, A. V. Dynamics of spatially chaotic solutions of parabolic equations. (English. Russian original) Zbl 0874.35046 Sb. Math. 186, No. 10, 1389-1415 (1995); translation from Mat. Sb. 186, No. 10, 3-30 (1995). From the author’s abstract: We study parabolic systems with a potential nonlinearity with one or many spatial variables. We describe a rather general and stable mechanism explaining the appearance and preservation of complicated stable spatial forms. The main idea consists in a description of the complexity of a solution in terms of its homotopy class. This class is a discrete-valued preserved quantity. Reviewer: M.Fila (Bratislava) Cited in 1 ReviewCited in 1 Document MSC: 35K45 Initial value problems for second-order parabolic systems 35B40 Asymptotic behavior of solutions to PDEs 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs Keywords:parabolic systems; complicated spatial structure; homotopy class PDFBibTeX XMLCite \textit{A. V. Babin}, Sb. Math. 186, No. 10, 1389--1415 (1995; Zbl 0874.35046); translation from Mat. Sb. 186, No. 10, 3--30 (1995) Full Text: DOI