(untitled) (Journal of Partial Differential Equations, 2014)
" We give an existence result of a renormalized solution for a class of nonlinear parabolic equations frac partial b(x,u) partial t-div(a(x,t,u, abla u))+g(x,t,u, abla u)+H(x,t, abla u)=f, qquad in ; Q_T, where the right side belongs to L^p'(0,T;W^-1,p'(03a9)) and where b(x,u) is unbounded function of u and where -div(a(x,t,u,2207u)) is a Leray-Lions type operatorwith growth |2207u|^p-1 in 2207u. The critical growth condition on g is with respect to 2207u and no growth condition with respect to u, while the function H(x,t,2207u) grows as |2207u|^p-1."