Author(s) :
Timo Reis
,
Caren Tischendorf
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 01-2005
MSC 2000
- 34A09 Implicit equations, differential-algebraic equations
-
34A30 Linear equations and systems, general
Abstract :
We discuss the analysis of constant coefficient linear
differential algebraic equations $E\dot{x}(t)=Ax(t)+q(t)$ on
infinite dimensional Hilbert spaces. We give solvability criteria
of these systems which are mainly based on Laplace transformation.
Furthermore, we investigate decoupling of these systems, motivated
by the decoupling of finite dimensional differential algebraic
systems by the Kronecker normal form. Applications are given by
the analysis of mixed systems of ordinary differential, partial
differential and differential algebraic equations.
Keywords :
partial differential-algebraic equations, index, infinite dimensional linear system theory