On some parabolic problems with measure sources

Abstract

One of the recent advances in the investigation of nonlinear parabolic equations with a measure as forcing term is a paper by F. Petitta in which it has been introduced the notion of renormalized solutions to the initial parabolic problem in divergence form. Here we continue the study of the stability of renormalized solutions to nonlinear parabolic equations with measures but from a different point of view: we investigate the existence and uniqueness of the following nonlinear initial boundary value problems with absorption term and a possibly sign-changing measure data

Keywords

• generalized solutions
• measures and capacities
• nonlinear parabolic equations
• pseudo-monotone operators
• stability
• primary 35k67
• 37k45
• 35a35
• 35s05
• 28a12