非游荡算子半群标准及应用 |
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引用本文: | 许华,王明刚. 非游荡算子半群标准及应用[J]. 数学的实践与认识, 2014, 0(5) |
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作者姓名: | 许华 王明刚 |
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作者单位: | 南京师范大学泰州学院; |
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基金项目: | 江苏省软科学项目(BR2013039);南京师范大学泰州学院青年项目(Q201233);南京师范大学泰州学院重点项目(Z201206);江苏省高校大学生创新训练计划项目(201313843012Y);泰州市科技支撑计划项目(TS201230);江苏省青蓝工程资助 |
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摘 要: | 根据非游荡算子半群的定义得到了非游荡算子半群的几个性质,给出了判定算子半群是非游荡半群的标准,应用给出的标准,在空间C([0,1],C)上讨论了偏微分方程au/at=γx(au/ax)+h(x)u,u(0,x)=f(x)的解半群的性质.
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关 键 词: | 非游荡半群 超循环半群 混沌半群 偏微分方程算子 |
Non-wandering for the Solution Semi-Groups to Certain Partial Differential Equations |
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Abstract: | In the research of dynamic system,the concept of the non-wandering semigroup is relative to hypercyclic semigroup and chaotic semigroup.In this paper,we consider the initial value problem of a partial differential equation au/at=c(x)au/ax+g(x,u) in some function spaces X_1 on the interval I of the real line.We give sufficient conditions for the solution semigroup to be Non-wandering semigroup by using the spectral property of its infinitesimal generator. |
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Keywords: | non-wandering semigroup hypercyclic semigroup chaotic semigroup partial differential operators |
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