Abstract :
This paper is concerned with the abstract degenerate Cauchy problemŽDCP.,
ddt BuŽt. AuŽt. Žt 0., BuŽ0. Bu0 , where A and B are closed linear operators
in a sequentially complete locally convex space. A C-propagation family forŽDCP.
is introducedŽC is an operator., leading to a general C-wellposedness result about
ŽDCP.. Moreover, conditions are given ensuring the existence of C-propagation
families for thoseŽDCP.with differential operators, on various function spaces
with Fr´echet topologies, as coefficient operators. These results are new even in the
case of Banach spaces.
