Existence of a solution for a class of parabolic equations with three unbounded nonlinearities, natural growth terms and L 1 data

摘要

We give an existence result of a renormalized solution for a class of nonlinear parabolic equations ? b ( x , u ) ? t - div ( a ( x , t , u , ? u ) ) + g ( u ) | ? u | p = f , where the right side belongs to L 1 (Ω × (0, T )), b ( x , u ) is an unbounded function of u and ?div( a ( x , t , u , ? u )) is a Leray–Lions type operator with growth ∣? u ∣ p ?1 in ? u , but without any growth assumption on u . The function g is just assumed to be continuous on R and satisfying a sign condition.