The heat semigroup on sectorial domains, highly singular initial values and applications

被引：8

作者：

Mouajria, Hattab ^{[1
]}

Tayachi, Slim ^{[1
]}

Weissler, Fred B. ^{[2
]}

机构：

[1] Univ Tunis El Manar, Lab Equat Derivees Partielles LR03ES04, Dept Math, Fac Sci Tunis, Tunis 2092, Tunisia

[2] Univ Paris 13, Sorbonne Paris Cite, CNRS, UMR LAGA 7539, 99 Ave Jean Baptiste Clement, F-93430 Villetaneuse, France

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2016年 / 16卷 / 02期

关键词：

Heat equation; Complexity; Sectorial domains; Asymptotic behavior; Antisymmetric solutions; Scaling; MULTISCALE ASYMPTOTIC-BEHAVIOR; COMPLEXITY; EQUATIONS;

D O I：

10.1007/s00028-015-0305-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the heat semigroup is well defined on the Banach space , where . We then investigate the large time behavior of solutions of the heat equation for t > 0 and Using certain notions from dynamical systems, we show that the large time behavior is related to the spatial asymptotic behavior of its initial value. Since the space contains highly singular initial data, which can be extended to all of by antisymmetry, we also obtain new results on the complexity in the asymptotic behavior of solutions for the heat equation on the whole space.

引用

页码：341 / 364

页数：24

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