压缩映射原理在方程解研究中的两种形式及证明

Two Forms and Proofs of the Compression Mapping Principle in the Research of the Solutions to the Equations

进一步阐明压缩映射原理在具非线性源项的偏微分方程初边值问题整体解的存在性及唯一性研究中的作用,列出此原理常用的几种形式,并给出证明.在理论和工程技术应用上,清晰解释了压缩映射理论的内部原理,证明了解的初值对整体解存在唯一性的影响,即整体解对初值的连续依赖性.这一讨论和分析清晰地说明了压缩映射原理处理问题的内部原理.

In this article the compression mapping principle in the research of existence and uniqueness of solutions to the initial boundary value problem of partial differential equations with nonlinear source terms is further explained. Several forms and proofs of the principle are also studied. In theo-retical and engineering applications,the internal principle of the compression mapping principle is clearly explained. It is proved that the initial value effects the existence and uniqueness of the solutions. That is the global solutions de pend on continuously the initial value. This discussion and analysis explain clearly the internal principle of dealing with the problem by the compression mapping principle.