On solvability of dissipative partial differential-algebraic equations

Birgit Jacob; Kirsten Morris

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arXiv · 2204.10599

On solvability of dissipative partial differential-algebraic equations

Birgit Jacob·Kirsten Morris

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Abstract

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.

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Birgit Jacob, Kirsten Morris. 2022-04-22. On solvability of dissipative partial differential-algebraic equations. https://arxiv.org/abs/2204.10599

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