A family of nonlinear fourth order equations of gradient flow type

Matthes Daniel, Robert J. McCann, Giuseppe Savaré

Research output: Contribution to journalArticlepeer-review

114 Scopus citations

Abstract

Global existence and long-time behavior of solutions to a family of nonlinear fourth order evolution equations on Rd are studied. These equations constitute gradient flows for the perturbed information functionals with respect to the L2-Wasserstein metric. The value of α ranges from α = 1/2, corresponding to a simplified quantum drift diffusion model, to α = 1, corresponding to a thin film type equation.

Original languageEnglish
Pages (from-to)1352-1397
Number of pages46
JournalCommunications in Partial Differential Equations
Volume34
Issue number11
DOIs
StatePublished - Nov 2009
Externally publishedYes

Keywords

  • Entropy method
  • Fourth-order equations
  • Gradient flow
  • Nonlinear parabolic equations
  • References
  • Wasserstein distance

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