A Widder's Type Theorem for the Heat Equation with Nonlocal Diffusion

Begoña Barrios, Ireneo Peral, Fernando Soria, Enrico Valdinoci

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

The main goal of this work is to prove that every non-negative strong solution u(x, t) to the problem (Formula presented.) can be written as (Formula presented.) where (Formula presented.) and (Formula presented.) This result shows uniqueness in the setting of non-negative solutions and extends some classical results for the heat equation by Widder in [15] to the nonlocal diffusion framework.

Original languageEnglish
Pages (from-to)629-650
Number of pages22
JournalArchive for Rational Mechanics and Analysis
Volume213
Issue number2
DOIs
Publication statusPublished - 1 Jan 2014
Externally publishedYes

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