On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditions

被引：1

作者：

Kalita, Piotr ^{[1
]}

Zgliczynski, Piotr ^{[1
]}

机构：

[1] Jagiellonian Univ, Fac Math & Comp Sci, Ul Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2020年 / 150卷 / 04期

关键词：

Burgers equation; non-autonomous forcing; asymptotic behaviour; global stability; eternal solution; energy method; maximum principle; pullback attractor; EXISTENCE;

D O I：

10.1017/prm.2019.11

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the non-autonomously forced Burgers equation on the space interval (0, 1) with two sets of the boundary conditions: the Dirichlet and periodic ones. For both situations we prove that there exists the unique /11 bounded trajectory of this equation defined for all t E B. Moreover we demonstrate that this trajectory attracts all trajectories both in pullback and forward sense. We also prove that for the Dirichlet case this attraction is exponential.

引用

页码：2025 / 2054

页数：30

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