Long-time behavior for a nonlinear fourth-order parabolic equation

María J. Cáceres, J. A. Carrillo, G. Toscani

Research output: Contribution to journalArticleResearchpeer-review

36 Citations (Scopus)


We study the asymptotic behavior of solutions of the initial-boundary value problem, with periodic boundary conditions, for a fourth-order nonlinear degenerate diffusion equation with a logarithmic nonlinearity. For strictly positive and suitably small initial data we show that a positive solution exponentially approaches its mean as time tends to infinity. These results are derived by analyzing the equation verified by the logarithm of the solution. © 2004 American Mathematical Society.
Original languageEnglish
Pages (from-to)1161-1175
JournalTransactions of the American Mathematical Society
Publication statusPublished - 1 Mar 2005


  • Asymptotic behavior
  • Degenerate parabolic equation
  • Diffusion equation
  • Entropy dissipation


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