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### Existence result for nonlinear parabolic problems with L¹-data

Applicationes Mathematicae

We study the existence of solutions of the nonlinear parabolic problem $\partial u/\partial t-div\left[|Du-\Theta \left(u\right){|}^{p-2}\left(Du-\Theta \left(u\right)\right)\right]+\alpha \left(u\right)=f$ in ]0,T[ × Ω, $\left(|Du-\Theta \left(u\right){|}^{p-2}\left(Du-\Theta \left(u\right)\right)\right)·\eta +\gamma \left(u\right)=g$ on ]0,T[ × ∂Ω, u(0,·) = u₀ in Ω, with initial data in L¹. We use a time discretization of the continuous problem by the Euler forward scheme.

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