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In this paper we study existence and uniqueness of solutions for the boundary-value problem, with initial datum in      L 1 ( Ω  ) L^{1}(\Omega )      ,      u t = d i v a ( x , D u ) in  ( 0 , ∞  ) ×  Ω  , \begin{equation*}u_{t} = \mathrm {div} \mathbf {a} (x,Du) \quad \text {in } (0, \infty ) \times \Omega , \end{equation*}            −  ∂  u ∂  η  a ∈  β  ( u ) on  ( 0 , ∞  ) ×  ∂  Ω  , \begin{equation*}-{\frac {{\partial u} }{{\partial \eta _{a}}}} \in \beta (u) \quad \text {on } (0, \infty ) \times \partial \Omega ,\end{equation*}            u ( x , 0 ) = u 0 ( x ) in  Ω  , \begin{equation*}u(x, 0) = u_{0}(x) \quad \text {in }\Omega ,\end{equation*}       where  a  is a Carathéodory function satisfying the classical Leray-Lions hypothesis,      ∂  / ∂  η  a \partial / {\partial \eta _{a}}       is the Neumann boundary operator associated to      a \mathbf {a}      ,      D u Du       the gradient of      u u       and      β  \beta       is a maximal monotone graph in      R ×  R {\mathbb {R}}\times {\mathbb {R}}       with      0 ∈  β  ( 0 ) 0 \in \beta (0)      .

Existence and uniqueness for a degenerate parabolic equation with 𝐿¹-data