European Journal of Applied Mathematics

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

a1 Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain


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)