Renormalized solution of nonlinear parabolic equations without sign condition and general measure data

Abstract

We give an existence result of a renormalized solution for a class of nonlinear parabolic equations (∂b(u) ∕ ∂ t) - div (a(x, t, ∇ u)) + h(u) |∇u|^p = μ, where the right side is a general measure and b(u) is a strictly increasing C¹-function with b(0)=0, - div(a(x, t, ∇ u)) is a Leray--Lions type operator with growth |∇u|^p-1 in ∇ u and h: ℝ → ℝ⁺ is a continuous positive function that belongs to L¹(ℝ).