Pseudo-Parabolic Regularization of Forward-Backward Parabolic Equations with Bounded Nonlinearities
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with Radon measure-valued initial data, by assuming that the regularizing term ψ is bounded and increasing (the cases of power-type or logarithmic ψ were examined in [2, 3] for spaces on any dimension). The function 𝜑 is nonmonotone and bounded, and either (i) decreases and vanishes at infinity, or (ii) increases at infinity. The existence of solutions in a space of positive Radon measures is proved in both cases. Moreover, a general result on the spontaneous appearance of singularities in he case (i) is presented. The case of a cubic-like 𝜑 is also discussed to point out the influence of the behavior at infinity of 𝜑 on the regularity of solutions.
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