A few results on some nonlinear parabolic problems in Orlicz-Sobolev spaces

In this paper, we present our results (see our papers), which concern the existence of the renormalized solutions for equations of the type:

∂b(x,u)∂t-div(a(x,t,u,∇u))-div(Φ(x,t,u))=f in Q=Ω×(0,T),$${{\partial b(x,u)} \over {\partial t}} - {\rm{div}}\left( {a(x,t,u,\nabla u)} \right) - {\rm{div}}\left( {\Phi \left( {x,t,u} \right)} \right) = f\,\,\,{\rm{in}}\,Q = \Omega \times (0,T),$$

where b(x, ·) is a strictly increasing C¹-function for any x ∈ Δ, a(x, t, s, ξ) and Φ(x, t, s) are a Carathéodory functions. The function f is in L¹(Q).