Pseudo-Parabolic Regularization of Forward-Backward Parabolic Equations with Bounded Nonlinearities


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Abstract

We study the initial-boundary value problem, with Radon measure-valued initial data, by assuming that the regularizing term ψ is increasing and bounded (the cases of power-type or logarithmic ψ were dealt with in [2, 3] in any space dimension). The function ϕ is nonmonotone and bounded, and either (i) decreasing and vanishing at in nity, or (ii) increasing at in nity. Existence of solutions in a space of positive Radon measures is proven in both cases. Moreover, a general result proving spontaneous appearance of singularities in case (i) is given. The case of a cubic-like ϕ is also discussed, to point out the in uence of the behavior at in nity of ϕ on the regularity of solutions.

About the authors

Alberto Tesei

Istituto per le Applicazioni del Calcolo «M. Picone» Consiglio Nazionale delle Ricerche

Email: albertotesei@gmail.com
Rome, Italy

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