The thin-film equation close to self-similarity

Seis, Christian

doi:10.2140/apde.2018.11.1303

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1948-206X (online)

ISSN 2157-5045 (print)

Author index

To appear

Other MSP journals

The thin-film equation close to self-similarity

Christian Seis

Vol. 11 (2018), No. 5, 1303–1342

DOI: 10.2140/apde.2018.11.1303

Abstract

We study well-posedness and regularity of the multidimensional thin-film equation with linear mobility in a neighborhood of the self-similar Smyth–Hill solutions. To be more specific, we perform a von Mises change of dependent and independent variables that transforms the thin-film free boundary problem into a parabolic equation on the unit ball. We show that the transformed equation is well-posed and that solutions are smooth and even analytic in time and angular direction. The latter gives the analyticity of level sets of the original equation, and thus, in particular, of the free boundary.

Keywords

thin-film equation, fourth-order equation, self-similar solution, well-posedness

Mathematical Subject Classification 2010

Primary: 35K30

Secondary: 76A20

Milestones

Received: 5 September 2017

Accepted: 2 January 2018

Published: 11 April 2018

Authors

Christian Seis
Institut für Analysis und Numerik Westfälische Wilhelms-Universität Münster Münster Germany

Vol. 11, No. 5, 2018