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Dissipative Dynamics for a Class of Nonlinear Pseudo-Differential Equations

โœ Scribed by M. Frankel; V. Roytburd


Publisher
Springer
Year
2008
Tongue
English
Weight
194 KB
Volume
8
Category
Article
ISSN
1424-3199

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We study a class of nonlinear evolutionary equations generated by a pseudo-differential operator with the elliptic principal symbol and with nonlinearities of the form G(u x ) where cฮท 2 โ‰ค G(ฮท) โ‰ค Cฮท 2 for large |ฮท|. We demonstrate existence of a universal absorbing set, and a compact attractor, and

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## It is a difficult problem to establish useful results on positivity of solutions of semilinear dissipative partial differential equations containing differential operators of order higher than that of the Laplacian. Positivity results are of importance in some fields of applied mathematics, suc