A periodic boundary value problem for a generalized 2D Ginzburg-Landau equation

Периодическая Задача Для Нелинейного Уравнения Соболева

“…Некоторые оценки убывания реше-ний уравнения Кортевега-де Фриза-Бюргерса с периодическими начальными данными, имеющими нулевое среднее значение, найдены в [15], где было пока-зано также, что асимптотическое поведение определяется гармониками более высокого порядка. В [16] доказано существование единственного глобального по времени решения периодической задачи для уравнения Ландау-Гинзбурга, а также получены оценки убывания по времени в различных нормах. Явные периодические решения уравнения Ландау-Гинзбурга найдены в [27].…”

Periodic boundary value problem for nonlinear Sobolev-type equations

“…Some decay estimates for solutions of the Korteweg-de Vries-Burgers equation with zero-mean space-periodic initial data are given in [15]; it was also shown in [15] that the asymptotic behavior is determined by higher harmonics. In [16], the existence and uniqueness of a global-in-time solution to the periodic problem for the Landau-Ginzburg equation was proved and decay in time was estimated in various norms. Explicit periodic solutions to the Landau-Ginzburg equation were found in [27].…”

Asymptotics of solutions to the periodic problem for a Burgers type equation

“…Some time decay estimates of solutions of the Korteweg-de Vries-Burgers equation with periodic initial data with zero mean value were found in paper [2], where it was shown also that the asymptotic behavior is defined by the higher-order harmonics. The existence of unique global solutions for the periodic problem to LandauGinzburg equation was proved in papers [3,9,27]. Also, time decay estimates of solutions in different norms were obtained, and the blow up phenomena were studied for the case of large initial data.…”