Submitted Paper
Inserted: 11 sep 2002
Last Updated: 31 oct 2003
Year: 2002
Abstract:
We give an existence result for the evolution equation
$(R u)' + A u = f$ in the space
$W = \{ u \in V \
\ (R u)' \in V' \}$ where $V$ is a Banach space
and $R$ is a non-invertible operator
(the equation may be partially elliptic and partially parabolic, both
forward and backward) and we study the ``Cauchy-Dirichlet'' problem
associated to this equation (indeed also for the inclusion
$(R u)' + A u \ni f$).
We also investigate continuous and compact embeddings of $W$
and regularity in time of the solution. At the end we give some examples
of different $R$.
Download: