Index concepts for linear differential-algebraic equations in finite and infinite dimensions
arxiv(2024)
摘要
Different index concepts for linear differential-algebraic equations are
defined in the general Banach space setting, and compared. For regular
finite-dimensional linear differential-algebraic equations, all these indices
exist and are equivalent. For infinite-dimensional systems, the situation is
more complex. It is proven that although some indices imply others, in general
they are not equivalent. The situation is illustrated with a number of
examples.
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