\(L^{2}\)-norm blow-up of solutions to a fourth order parabolic PDE involving the Hessian
type: Item
instance of: scholarly article
title: \(L^{2}\)-norm blow-up of solutions to a fourth order parabolic PDE involving the Hessian
zbMATH Open document ID: 1405.35074
author: Jun Zhou
published in: Journal of Differential Equations
publication date: 2018-09-06T00:00:00Z
review text: The author studies the initial-boundary value problem for the equation \(u_t+\Delta^2u=\text{det}\left(D^2u\right)\) describing the epitaxial growth of a crystal. An answer is given to an open question in [\textit{C. Escudero} et al., J. Math. Pures Appl. 103, 924--957 (2015; Zbl 1406.35114)] concerning possible blowups of solutions. The main result is an ubounded growth of the \(L^2\) norm of a solution emanating from data satisfying a condition on the energy functional associated with the stationary problem. These are also generalizations of results in [\textit{G. Xu} and \textit{J. Zhou}, NoDEA, Nonlinear Differ. Equ. Appl. 24, No. 4, Paper No. 41, 12 p. (2017; Zbl 1375.35240)].
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35J30
Mathematics Subject Classification ID: 35Q70
zbMATH DE Number: 6933424
zbMATH Keywords: fourth order parabolic PDE
zbMATH Keywords: epitaxial growth
zbMATH Keywords: blowup of solutions
MaRDI profile type: Publication
full work available at URL: j.jde.2018.06.015
OpenAlex ID: W2808734899
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DOI: 10.1016/J.JDE.2018.06.015
description: scientific article; zbMATH DE number 6933424