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

Begoña Barrios; Ireneo Peral; Fernando Soria; Enrico Valdinoci

doi:10.1007/s00205-014-0733-1

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

Begoña Barrios, Ireneo Peral, Fernando Soria, Enrico Valdinoci

Research output: Contribution to journal › Article

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 language	English
Pages (from-to)	629-650
Number of pages	22
Journal	Archive for Rational Mechanics and Analysis
Volume	213
Issue number	2
DOIs	https://doi.org/10.1007/s00205-014-0733-1
Publication status	Published - 1 Jan 2014
Externally published	Yes

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