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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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-05-01
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| Series: | Boundary Value Problems |
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| 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. |
| format | Article |
| id | doaj-art-e9ca1b52f05b4e9d8da934d81f5ac1f5 |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| 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 |