Porzio, Maria Michaela Regularity and time behavior of the solutions of linear and quasilinear parabolic equations. (English) Zbl 1390.35115 Adv. Differ. Equ. 23, No. 5-6, 329-372 (2018). Summary: In this paper, we study the regularity, the uniqueness and the asymptotic behavior of the solutions to a class of nonlinear operators in dependence of the summability properties of the datum \(f\) and of the initial datum \(u_0\). The case of only summable data \(f\) and \(u_0\) is allowed. We prove that these equations satisfy surprising regularization phenomena. Moreover, we prove estimates (depending continuously from the data) that for zero datum \(f\) become well known decay (or ultracontractive) estimates. Cited in 8 Documents MSC: 35K10 Second-order parabolic equations 35K59 Quasilinear parabolic equations 35D30 Weak solutions to PDEs PDFBibTeX XMLCite \textit{M. M. Porzio}, Adv. Differ. Equ. 23, No. 5--6, 329--372 (2018; Zbl 1390.35115) Full Text: Euclid