Entropy solutions for a nonlinear parabolic problems with lower order term in Orlicz spaces

Abstract

We shall give the proof of existence results for the entropy solutions of the following nonlinear parabolic problem Open image in new window where A is a Leray–Lions operator having a growth not necessarily of polynomial type. The lower order term \(\Phi \) :\(\Omega \times (0,T)\times \mathbb {R}\rightarrow \mathbb {R}^N\) is a Caratheodory function, for a.e. \((x,t)\in Q_T\) and for all \(s\in \mathbb {R}\), satisfying only a growth condition and the right hand side f belongs to \(L^1(Q_T)\).