AN ENTROPY DISSIPATION-ENTROPY ESTIMATE FOR A THIN FILM TYPE EQUATION*

E. A. Carlen, S. Ulusoy

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We prove a lower bound on the rate of relaxation to equilibrium in the H1 norm for a thin film equation. We find a two stage relaxation, with power law decay in an initial interval, followed by exponential decay, at an essentially optimal rate, for large times. The waiting time until the exponential decay sets in is explicitly estimated.

Original languageEnglish (US)
Pages (from-to)171-178
Number of pages8
JournalCommunications in Mathematical Sciences
Volume3
Issue number2
DOIs
StatePublished - 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Dissipation
  • Lyapunov functional
  • Thin films

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