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

    • Published online: 01 October 1997

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]).

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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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