Problems paraboliques semi-lineaires avec donnees measures

Abstract

We study semilinear evolution equation of the type :

where f and ν are given measures on ]o,T[ x ω and ω respectively, ω being a bounded open subset of IR^N . We showthat (P) has a solution if and only if f and ν are not to much "concentrated" and do not charge too thin sets : the precise content of the statement involves capacities associated with suitable Sobolev's spaces. The question of removability of singularities for (P) is also completely solved.

AMS(MOS):

• 35K55
• 35K22
• 31C15
• 31B35