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In this paper, we study existence, uniqueness and stability questions for the nonlinear parabolic equation: ∂u ∂t − pu + α(u )= fi n]0 ,T [×Ω, with Neumann-type boundary conditions and initial data in L 1 .O ur approach is based essentially on the time discretization technique by Euler forward scheme. 2000 Subject Classifications: 35K05, 35J55, 35D65.

Nonlinear parabolic problems with Neumann-type boundary conditions and L^1-data