WIAS Preprint No. 1798, (2013)

A Widder's type theorem for the heat equation with nonlocal diffusion



Authors

  • Barrios, Begoña
  • Peral, Ireneo
  • Soria, Fernando
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35K05 35K15 35C15 35B30 35B99

Keywords

  • Heat equation, fractional Laplacian, trace of strong solutions, uniqueness of non-negative solutions

Abstract

The main goal of this work is to prove that every non-negative strong solution of the fractional heat equation can be written as a kernel convolution with its initial datum. This result shows uniqueness in the setting of non-negative solutions and extends some classical results for the heat equation by D. V. Widder to the nonlocal diffusion framework.

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