Well-posedness for a slow erosion model

We improve in two ways the well-posedness results of [2] for a slow erosion model proposed in [11]: firstly we study the asymptotic profile when u01+u0∈L∞, where u0 is the initial datum; moreover, using a compensated compactness based argument we prove the existence of solutions when u01+u0∈Lσ, σ≥3.