Communications in Mathematical Physics

, Volume 225, Issue 3, pp 551–571 | Cite as

Long-Time Asymptotics for Strong Solutions¶of the Thin Film Equation

  • J. A. Carrillo
  • G. Toscani


In this paper we investigate the large-time behavior of strong solutions to the one-dimensional fourth order degenerate parabolic equation u t =−(u u xxx ) x , modeling the evolution of the interface of a spreading droplet. For nonnegative initial values u 0(x)∈H 1(ℝ), both compactly supported or of finite second moment, we prove explicit and universal algebraic decay in the L 1-norm of the strong solution u(x,t) towards the unique (among source type solutions) strong source type solution of the equation with the same mass. The method we use is based on the study of the time decay of the entropy introduced in [13] for the porous medium equation, and uses analogies between the thin film equation and the porous medium equation.


Entropy Porous Medium Time Decay Parabolic Equation Fourth Order 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • J. A. Carrillo
    • 1
  • G. Toscani
    • 2
  1. 1.Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, SpainES
  2. 2.Department of Mathematics, University of Pavia, via Ferrata 1, 27100 Pavia, ItalyIT

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