Nonlinear parabolic inequalities with lower order terms

Abstract

We prove an existence result of entropy solutions for the nonlinear parabolic problems with obstacle in and a.e. in where b(x, u) is a strictly increasing -function of u, the term is a Leray–Lions type operator and the function is a nonlinear lower order term and satisfies only growth condition. The data f belongs to . The proof is based on the penalization methods.