Hölder estimate for non-uniform parabolic equations in highly heterogeneous media

Li-Ming Yeh*

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Uniform bound for the solutions of non-uniform parabolic equations in highly heterogeneous media is concerned. The media considered are periodic and they consist of a connected high permeability sub-region and a disconnected matrix block subset with low permeability. Parabolic equations with diffusion depending on the permeability of the media have fast diffusion in the high permeability sub-region and slow diffusion in the low permeability subset, and they form non-uniform parabolic equations. Each medium is associated with a positive number ∈, denoting the size ratio of matrix blocks to the whole domain of the medium. Let the permeability ratio of the matrix block subset to the connected high permeability sub-region be of the order ∈ for τ ∈ (0,1]. It is proved that the Hölder norm of the solutions of the above non-uniform parabolic equations in the connected high permeability sub-region are bounded uniformly in . One example also shows that the Hölder norm of the solutions in the disconnected subset may not be bounded uniformly in ∈.

Original languageEnglish
Pages (from-to)3723-3745
Number of pages23
JournalNonlinear Analysis, Theory, Methods and Applications
Volume75
Issue number9
DOIs
StatePublished - 1 Jun 2012

Keywords

  • Highly heterogeneous media
  • Infinitesimal generator
  • Numerical range
  • Paramatrix
  • Pseudo-differential operator
  • Strict solution

Fingerprint Dive into the research topics of 'Hölder estimate for non-uniform parabolic equations in highly heterogeneous media'. Together they form a unique fingerprint.

  • Cite this