Abstract Degenerate Cauchy Problems in Locally Convex Spaces

Abstract This paper is concerned with the abstract degenerate Cauchy problem DCP , d dt Bu(t) = Au(t) (t ≥ 0), Bu(0) = Bu 0 , where A and B are closed linear operators in a sequentially complete locally convex space. A C-propagation family for (DCP) is introduced (C is an operator), leading to a general C-wellposedness result about (DCP). Moreover, conditions are given ensuring the existence of C-propagation families for those (DCP) with differential operators, on various function spaces with Frechet topologies, as coefficient operators. These results are new even in the case of Banach spaces.