### Bernd Thaller

Institut f. Mathematik

Universität Graz

A-8010 Graz, Austria

e-mail: bernd.thaller@kfunigraz.ac.at

## Approximation of Degenerate Cauchy Problems

### Authors:

Sigrid Thaller and Bernd Thaller

### Abstract:

We investigate the approximation of a linear homogenuous degenerate Cauchy problem d/dt Mz(t) = Az(t), z(0) = z0, where M and A are closed, densely defined operators in a Hilbert space and M has a nontrivial kernel. Analoguously to the Trotter-Kato Theory for nondegenerate equations we obtain conditions when the convergence of the pseudo resolvents of M and A is equivalent to the convergence of the solutions of the given Cauchy problem. We study the connection between these approximations and approximations of the factorized nondegenerate Cauchy problem connected with the given problem and we give an example where factorization and approximation can be interchanged.

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Bernd Thaller

Institute of Mathematics

University of Graz.

Page design of course by: Bernd Thaller.

last changed: 03-21-1997