Banach空间上一类二阶偏微分系统解的存在性

The existence of solutions for a second order partial differential system in Banach space

研究一类建立在Banach空间上的二阶齐次抽象偏微分系统解的存在性。运用强连续线性算子半群理论以及非线性泛函分析方法给出了系统存在解的充分性条件。结果表明,强连续线性算子半群的生成元与系统解的存在性之间有密切的关系。文中结论对于这类问题具有一般性,补充并推广了一些已有结果,所用方法对一些演化方程解的存在性问题具有一定的适用性。

The existence of solutions for a second order homogeneous partial differential system in Banach space is investigated.By using the theory of the strongly continuous semi-groups of linear operators and the method of nonlinear functional analysis,a sufficient condition on the existence of the solutions is given.The result shows that there are some close relationships between the generator of a strongly continuous semi-groups of linear operators and the existence of the solutions.A general conclusion on these problems is presented,it complements and generalizes some existing results,and the techniques used in this paper,to some extent,are applicable for the existence of solutions of some evolution equations.