Abstract degenerate Cauchy problems in locally convex spaces

摘要

This paper is concerned with the abstract degenerate Cauchy problem (DCP), d/dtBu(t) = Au(t) (t greater than or equal to 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, (C) 2001 Academic Press. [References: 15]