Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order

Buyang Li, Hong Wang, Jilu Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)

Abstract

We prove well-posedness and regularity of solutions to a fractional diffusion porous media equation with a variable fractional order that may depend on the unknown solution. We present a linearly implicit time-stepping method to linearize and discretize the equation in time, and present rigorous analysis for the convergence of numerical solutions based on proved regularity results.

Original languageEnglish
Pages (from-to)171-207
Number of pages37
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume55
Issue number1
DOIs
Publication statusPublished - 1 Jan 2021

Keywords

  • Convergence
  • Convolution quadrature
  • Fractional diffusion equation
  • Nonlinear
  • Numerical approximation
  • Regularity
  • Variable order
  • Well-posedness

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modelling and Simulation
  • Computational Mathematics
  • Applied Mathematics

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