Abstract
We study a class of nonlinear parabolic equations of the type: partial derivative b(u)/partial derivative t - div(a(x, t, u)del u) + g(u)vertical bar del u vertical bar(2) = f, where the right hand side belongs to L-1 (Q), b is a strictly increasing C-1-function and div(a(x, t, u)del u) is a Leray-Lions operator. The function g is just assumed to be continuous on R and to satisfy a sign condition. Without any additional growth assumption on u, we prove the existence of a renormalized solution.