We consider the following pseudoparabolic regularization of a forward-backward quasilinear diffusion equation: uₜ=Δφ(u)+εΔ uₜ (ε>0). As suggested byseveral models of the applied sciences, the function φ isnonmonotone and vanishing at infinity. We investigate the limitpoints of the set of solutions to the associated Neumann problem asε→ 0, proving existence of suitable weak solutions ofthe original ill-posed equation. Qualitative properties of suchsolutions are also addressed.
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Flavia Smarrazzo (2008) studied this question.
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