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
DOI
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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