Analysis of a nonlocal-in-time parabolic equation

Qiang Du, Jiang Yang, Zhi Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

17 Citations (Scopus)

Abstract

In this paper, we consider an initial boundary value problem for nonlocal-in-time parabolic equations involving a nonlocal in time derivative. We first show the uniqueness and existence of the weak solution of the nonlocal-in-time parabolic equation, and also the spatial smoothing properties. Moreover, we develop a new framework to study the local limit of the nonlocal model as the horizon parameter δ approaches 0. Exploiting the spatial smoothing properties, we develop a semi-discrete scheme using standard Galerkin finite element method for the spatial discretization, and derive error estimates dependent on data smoothness. Finally, extensive numerical results are presented to illustrate our theoretical findings.
Original languageEnglish
Pages (from-to)339-368
Number of pages30
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume22
Issue number2
DOIs
Publication statusPublished - 1 Mar 2017
Externally publishedYes

Keywords

  • Error estimates
  • Galerkin finite element method
  • Localization
  • Nonlocal initial value problem
  • Nonlocal-in-time parabolic equation
  • Smoothing property
  • Well-posedness

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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