Nonlinear dynamics of extended systems (Q2776594)

The author presents some recent ideas concerning the long time behavior of solutions to nonlinear parabolic equations in large unbounded domains. The lecture starts from the existence and regularity of the solutions involving parabolic maximum principle and a priori estimate technique with sample applications to Burgers equation and complex Ginzburg-Landau equation respectively. Then, the concept of attracting invariant sets is recalled, which considerations remain in the vein of \textit{A. Mielke} and \textit{G. Schneider} [Nonlinearity 8, 743-768 (1995; Zbl 0833.35016)]. Finally, in the last two parts of the lecture, some amplitude equations are constructed as well as the `large time asymptotic' discussion is given.NEWLINENEWLINEFor the entire collection see [Zbl 0977.00028].