文章基本信息

标题：Pullback attractors for non-autonomous reaction-diffusion equation in non-cylindrical domains
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作者：Yanping Xiao
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2016
卷号：2016
期号：1
页码：230
DOI：10.1186/s13662-016-0888-1
语种：English
出版社：Hindawi Publishing Corporation
摘要：In non-cylindrical domains, we use the definition of the variational solution and the maximum principle (the Galerkin method used usually in a cylindrical domain cannot be applied directly) to prove the existence of a pullback D λ 1 $\mathscr {D}_{\lambda_)}$ attractor in L p ( O t ) $L^{p}(\mathcal{O}_{t})$ (any p ⩾ 2 $p\geqslant 2$ ) for a reaction-diffusion equation. Then, with an appropriate assumption, the higher-order integrability of variational solution is obtained. Finally, we discuss the existence of a pullback D λ 1 $\mathscr{D}_{\lambda_)}$ attractor in L 2 + δ ( O t ) $L^{2+\delta}(\mathcal{O}_{t})$ for any δ ∈ [ 0 , + ∞ ) $\delta\in[0,+\infty)$ .
关键词：variational solution ; pullback $\mathscr{D}_{\lambda_)}$ attractor ; higher-order integrability ; non-cylindrical domains