Nonnegative solutions of a fourth-order nonlinear degenerate parabolic equation
type: Item
instance of: scholarly article
title: Nonnegative solutions of a fourth-order nonlinear degenerate parabolic equation
zbMATH Open document ID: 0827.35065
DOI: 10.1007/BF00379920
author: R. Dal Passo
author: Elena Beretta
author: Michiel Bertsch
published in: Archive for Rational Mechanics and Analysis
publication date: 1995-06-28T00:00:00Z
review text: The authors study nonnegative solutions of the equation \(u_t + (u^nu_{xxx})_x = 0\), where \(n\) is a real positive constant; the equation is degenerated at points \(x\) at which \(u\) vanishes. For \(0 < n < 1/2\), it is shown that initially strictly positive solutions may vanish at some point \(x_0\) after a finite time \(t_0\). This result is of particular interest for several hydrodynamic applications in which the above equation arises. For example, if \(u\) is interpreted as the thickness of a liquid film, it implies that at time \(t_0\) the film breaks at \(x_0\).
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 760206
zbMATH Keywords: vanishing of solutions at finite time
zbMATH Keywords: liquid film
MaRDI profile type: Publication
cites work: Q4027416
cites work: Higher order nonlinear degenerate parabolic equations
cites work: Source type solutions of a fourth order nonlinear degenerate parabolic equation
cites work: Q4297012
cites work: The Motion with Slip of a Thin Viscous Droplet over a Solid Surface
cites work: Some a Priori Estimates for a Singular Evolution Equation Arising in Thin-Film Dynamics
cites work: Q4884681
cites work: The lubrication approximation for thin viscous films: the moving contact line with a 'porous media' cut-off of van der Waals interactions
full work available at URL: https://doi.org/10.1007/bf00379920
OpenAlex ID: W2078279585
description: scientific article; zbMATH DE number 760206