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 i...

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Main Authors: Nikolaos M. Ladas, John C. Meyer
Format: Article
Language:English
Published: SpringerOpen 2025-05-01
Series:Boundary Value Problems
Subjects:
Online Access:https://doi.org/10.1186/s13661-025-02058-y
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author Nikolaos M. Ladas
John C. Meyer
author_facet Nikolaos M. Ladas
John C. Meyer
author_sort Nikolaos M. Ladas
collection DOAJ
description 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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spelling doaj-art-e9ca1b52f05b4e9d8da934d81f5ac1f52025-08-20T03:48:18ZengSpringerOpenBoundary Value Problems1687-27702025-05-012025113110.1186/s13661-025-02058-yMinimum and comparison principles for semilinear nonlocal reaction–diffusion equationsNikolaos M. Ladas0John C. Meyer1School of Mathematics, University of BirminghamSchool of Mathematics, University of BirminghamAbstract 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.https://doi.org/10.1186/s13661-025-02058-yMinimum principlesComparison PrinciplesNonlinear nonlocal integrodifferential operatorIntegrodifferential inequality
spellingShingle Nikolaos M. Ladas
John C. Meyer
Minimum and comparison principles for semilinear nonlocal reaction–diffusion equations
Boundary Value Problems
Minimum principles
Comparison Principles
Nonlinear nonlocal integrodifferential operator
Integrodifferential inequality
title Minimum and comparison principles for semilinear nonlocal reaction–diffusion equations
title_full Minimum and comparison principles for semilinear nonlocal reaction–diffusion equations
title_fullStr Minimum and comparison principles for semilinear nonlocal reaction–diffusion equations
title_full_unstemmed Minimum and comparison principles for semilinear nonlocal reaction–diffusion equations
title_short Minimum and comparison principles for semilinear nonlocal reaction–diffusion equations
title_sort minimum and comparison principles for semilinear nonlocal reaction diffusion equations
topic Minimum principles
Comparison Principles
Nonlinear nonlocal integrodifferential operator
Integrodifferential inequality
url https://doi.org/10.1186/s13661-025-02058-y
work_keys_str_mv AT nikolaosmladas minimumandcomparisonprinciplesforsemilinearnonlocalreactiondiffusionequations
AT johncmeyer minimumandcomparisonprinciplesforsemilinearnonlocalreactiondiffusionequations