The Calderón problem for a space-time fractional parabolic equation

Ru Yu Lai, Yi Hsuan Lin, Angkana Rüland

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this article we study an inverse problem for the space-time fractional parabolic operator (∂t - Δ)s + Q with 0 < s < 1 in any space dimension. We uniquely determine the unknown bounded potential Q from infinitely many exterior Dirichlet-to-Neumann type measurements. This relies on Runge approximation and the dual global weak unique continuation properties of the equation under consideration. In discussing weak unique continuation of our operator, a main feature of our argument relies on a new Carleman estimate for the associated degenerate parabolic Caffarelli- Silvestre extension. Furthermore, we also discuss constructive single measurement results based on the approximation and unique continuation properties of the equation.

Original languageEnglish
Pages (from-to)2655-2688
Number of pages34
JournalSIAM Journal on Mathematical Analysis
Volume52
Issue number3
DOIs
StatePublished - 2020

Keywords

  • Carleman estimate
  • Degenerate parabolic equations
  • Fractional parabolic Calderón problem
  • Nonlocal
  • Runge approximation
  • Unique continuation property

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