Minimum and comparison principles for semilinear nonlocal reaction–diffusion equations

Nikolaos Michael Ladas; John Christopher Meyer

doi:10.1186/s13661-025-02058-y

Minimum and comparison principles for semilinear nonlocal reaction–diffusion equations

Nikolaos Michael Ladas
, John Christopher Meyer^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

We consider second-order linear parabolic partial differential inequalities that include nonlocal zeroth-order quantities. For these, we establish minimum principles that highlight the interplay between the regularity of their coefficients, the growth/decay rate of their solutions and the integrability of the nonlocal interaction terms. Subsequently we utilize these minimum principles to establish comparison principles for related semilinear integrodifferential inequalities. We illustrate these principles via their relation to nonlocal reaction–diffusion equations.

Original language	English
Article number	72
Number of pages	31
Journal	Boundary Value Problems
Volume	2025
Issue number	1
DOIs	https://doi.org/10.1186/s13661-025-02058-y
Publication status	Published - 20 May 2025

Keywords

Minimum Principles
Comparison Principles
Nonlinear Nonlocal Integrodifferential Operator
Integrodifferential Inequality

ASJC Scopus subject areas

Analysis

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10.1186/s13661-025-02058-yLicence: Creative Commons: Attribution (CC BY)

LadasN2025MinimumFinal published version, 1.77 MBLicence: Creative Commons: Attribution (CC BY)

Extended weak maximum principles for parabolic partial differential inequalities on unbounded domains
Meyer, J. C. & Needham, D. J., 8 Jul 2014, In: Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences. 470, 2167, 20140079.
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Cite this

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title = "Minimum and comparison principles for semilinear nonlocal reaction–diffusion equations",

abstract = "We consider second-order linear parabolic partial differential inequalities that include nonlocal zeroth-order quantities. For these, we establish minimum principles that highlight the interplay between the regularity of their coefficients, the growth/decay rate of their solutions and the integrability of the nonlocal interaction terms. Subsequently we utilize these minimum principles to establish comparison principles for related semilinear integrodifferential inequalities. We illustrate these principles via their relation to nonlocal reaction–diffusion equations.",

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N2 - We consider second-order linear parabolic partial differential inequalities that include nonlocal zeroth-order quantities. For these, we establish minimum principles that highlight the interplay between the regularity of their coefficients, the growth/decay rate of their solutions and the integrability of the nonlocal interaction terms. Subsequently we utilize these minimum principles to establish comparison principles for related semilinear integrodifferential inequalities. We illustrate these principles via their relation to nonlocal reaction–diffusion equations.

AB - We consider second-order linear parabolic partial differential inequalities that include nonlocal zeroth-order quantities. For these, we establish minimum principles that highlight the interplay between the regularity of their coefficients, the growth/decay rate of their solutions and the integrability of the nonlocal interaction terms. Subsequently we utilize these minimum principles to establish comparison principles for related semilinear integrodifferential inequalities. We illustrate these principles via their relation to nonlocal reaction–diffusion equations.

KW - Minimum Principles

KW - Comparison Principles

KW - Nonlinear Nonlocal Integrodifferential Operator

KW - Integrodifferential Inequality

U2 - 10.1186/s13661-025-02058-y

DO - 10.1186/s13661-025-02058-y

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JO - Boundary Value Problems

JF - Boundary Value Problems

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ER -

Minimum and comparison principles for semilinear nonlocal reaction–diffusion equations

Abstract

Keywords

ASJC Scopus subject areas

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Research output

Extended weak maximum principles for parabolic partial differential inequalities on unbounded domains

Cite this