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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.

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
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