European Journal of Applied Mathematics



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


RAUL FERREIRA a1 and FRANCISCO BERNIS a1
a1 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[gt-or-equal, slanted]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[gt-or-equal, slanted]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]).

(Received September 29 1996)
(Revised January 27 1997)