Hostname: page-component-7c8c6479df-8mjnm Total loading time: 0 Render date: 2024-03-28T14:36:46.768Z Has data issue: false hasContentIssue false

Source-type solutions to thin-film equations in higher dimensions

Published online by Cambridge University Press:  01 October 1997

RAUL FERREIRA
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
FRANCISCO BERNIS
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Abstract

We prove that the thin film equation ht+div (hn grad (Δh))=0 in dimension d[ges ]2 has a unique C1 source-type radial self-similar non-negative solution if 0<n<3 and has no solution of this type if n[ges ]3. When 0<n3 the solution h has finite speed of propagation and we obtain the first order asymptotic behaviour of h at the interface or free boundary separating the regions where h>0 and h=0. (The case d=1 was already known [1]).

Type
Research Article
Copyright
© 1997 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)