Author:
de Bonis Ida,Porzio Maria Michaela
Abstract
AbstractIn this paper we prove existence and regularity results for a class of parabolic problems with irregular initial data and lower order terms singular with respect to the solution. We prove that, even if the initial datum is not bounded but only in $$L^1(\Omega )$$
L
1
(
Ω
)
, there exists a solution that “instantly” becomes bounded. Moreover we study the behavior in time of these solutions showing that this class of problems admits global solutions which all have the same behavior in time independently of the size of the initial data.
Funder
Università degli Studi di Roma La Sapienza
Publisher
Springer Science and Business Media LLC
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