We study a class of nonlinear parabolic equations of the type:b(u)t- div a(x, t, u)▽u + g(u)|▽u|2= f,where the right hand side belongs to L1(Q), b is a strictly increasing C1-function and-div(a(x, t, u)▽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.
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