Pseudo-Parabolic Regularization of Forward-Backward Parabolic Equations with Bounded Nonlinearities
- Authors: Tesei A.1
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Affiliations:
- Istituto per le Applicazioni del Calcolo “M. Picone,”, Consiglio Nazionale delle Ricerche
- Issue: Vol 235, No 4 (2018)
- Pages: 536-555
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242140
- DOI: https://doi.org/10.1007/s10958-018-4084-6
- ID: 242140
Cite item
Abstract
We study the initial-boundary value problem
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 ???? 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 ???? is also discussed to point out the influence of the behavior at infinity of ???? on the regularity of solutions.
About the authors
A. Tesei
Istituto per le Applicazioni del Calcolo “M. Picone,”, Consiglio Nazionale delle Ricerche
Author for correspondence.
Email: albertotesei@gmail.com
Italy, Rome