The chaos of the solution semigroup for some partial differential equations in weighted Banach spaces

Advances in Difference Equations

Xiangdong Yang¹ 

[1] Department of Mathematics, Kunming University of Science and Technology, Kunming, China

关键词: partial differential equation;    weighted Banach spaces;    chaos;    Carleman’s formula;   

DOI  :  10.1186/1687-1847-2014-123

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper we deal with the solution semigroup of some partial differential equations in a weighted Banach space on the real axis. We aim at showing the connection between complex-analytic approach and chaotic theory. With the approach of Carleman’s formula and Joel H Shapiro’s construction, we could construct dense systems of functions from which the chaos of the solution semigroup follows. The novelty of our paper is the usage of the complex-analytic approach in investigation on chaos of some partial differential equations. As far as we know, our manuscript is the first paper in this direction. MSC:35K30, 30E20.

【 授权许可】

CC BY