论文标题
关于耗散部分差分 - 代数方程的溶解度
On solvability of dissipative partial differential-algebraic equations
论文作者
论文摘要
在本文中，我们研究了无限维差分方程的可溶性。这种方程通常是作为部分差分 - 代数方程（PDAE）出现的。描述了这些方程式在希尔伯特空间上延伸的状态空间的分解。对于耗散偏微分方程，著名的Lumer-Phillips生成定理表征了相关半群的可溶性和界限。给出了向耗散差异代数方程式的腔内菲利普斯生成定理的扩展。耦合系统和Dzektser方程说明了结果。
In this article we investigate the solvability of infinite-dimensional differential algebraic equations. Such equations often arise as partial differential-algebraic equations (PDAEs). A decomposition of the state-space that leads to an extension of the Hille-Yosida Theorem on Hilbert spaces for these equations is described. For dissipative partial differential equations the famous Lumer-Phillips generation theorem characterizes solvability and also boundedness of the associated semigroup. An extension of the Lumer-Phillips generation theorem to dissipative differential-algebraic equations is given. The results is illustrated by coupled systems and the Dzektser equation.
