Abstract
In this paper we present a straightforward application of semigroup theory to degenerate Cauchy problems given by a pair of linear operators (A,M) defined in a Banach space. We prove existence and uniqueness of strict solutions for initial values contained in suitable subspaces under very mild conditions on the operators A and M . Furthermore, we describe the factorization with respect to KerM . A canonical example for the necessity of this procedure is provided by the Dirac equation in the nonrelativistic limit. The relation between the factorized problem and the degenerate problem is given by a mapping Z. We give simple examples showing that, in general, Z is unbounded and not even closable.
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