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Remarks on a Smoluchowski equation. (English) Zbl 1138.35336
Summary: We study the long time dynamics of a Smoluchowski equation arising in the modeling of nematic liquid crystalline polymers. We prove uniform bounds for the long time average of gradients of the distribution function in terms of the nondimensional parameter characterizing the intensity of the potential. In the two-dimensional case we obtain lower and upper bounds for the number of steady states. We prove that the system is dissipative and that the potential serves as unique determining mode of the system.

MSC:
35K35 Initial-boundary value problems for higher-order parabolic equations
76A15 Liquid crystals
82D30 Statistical mechanical studies of random media, disordered materials (including liquid crystals and spin glasses)
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