A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations

We consider a class of nonlinear integro-differential equations that model degenerate nonlocal diffusion. We investigate whether the strong maximum principle is valid for this nonlocal equation. For degenerate parabolic PDEs, the strong maximum principle is not valid. In contrast, for nonlocal diffu...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Tucker Hartland [verfasserIn] Ravi Shankar [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	nonlocal diffusion nonlinear diffusion integro-differential equations maximum principle strong maximum principle degenerate

Übergeordnetes Werk:	In: Axioms - MDPI AG, 2012, 12(2023), 11, p 1059
Übergeordnetes Werk:	volume:12 ; year:2023 ; number:11, p 1059

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/axioms12111059

Katalog-ID:	DOAJ10127534X

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allfields	10.3390/axioms12111059 doi (DE-627)DOAJ10127534X (DE-599)DOAJ46bd3234c59e40fb98fbb85ba6c95d98 DE-627 ger DE-627 rakwb eng QA1-939 Tucker Hartland verfasserin aut A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We consider a class of nonlinear integro-differential equations that model degenerate nonlocal diffusion. We investigate whether the strong maximum principle is valid for this nonlocal equation. For degenerate parabolic PDEs, the strong maximum principle is not valid. In contrast, for nonlocal diffusion, we can formulate a strong maximum principle for nonlinearities satisfying a geometric condition related to the flux operator of the equation. In our formulation of the strong maximum principle, we find a physical re-interpretation and generalization of the standard PDE conclusion of the principle: we replace constant solutions with solutions of zero flux. We also consider nonlinearities outside the scope of our principle. For highly degenerate conductivities, we demonstrate the invalidity of the strong maximum principle. We also consider intermediate, inconclusive examples, and provide numerical evidence that the strong maximum principle is valid. This suggests that our geometric condition is sharp. nonlocal diffusion nonlinear diffusion integro-differential equations maximum principle strong maximum principle degenerate Mathematics Ravi Shankar verfasserin aut In Axioms MDPI AG, 2012 12(2023), 11, p 1059 (DE-627)718622030 (DE-600)2661511-3 20751680 nnns volume:12 year:2023 number:11, p 1059 https://doi.org/10.3390/axioms12111059 kostenfrei https://doaj.org/article/46bd3234c59e40fb98fbb85ba6c95d98 kostenfrei https://www.mdpi.com/2075-1680/12/11/1059 kostenfrei https://doaj.org/toc/2075-1680 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 12 2023 11, p 1059
spelling	10.3390/axioms12111059 doi (DE-627)DOAJ10127534X (DE-599)DOAJ46bd3234c59e40fb98fbb85ba6c95d98 DE-627 ger DE-627 rakwb eng QA1-939 Tucker Hartland verfasserin aut A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We consider a class of nonlinear integro-differential equations that model degenerate nonlocal diffusion. We investigate whether the strong maximum principle is valid for this nonlocal equation. For degenerate parabolic PDEs, the strong maximum principle is not valid. In contrast, for nonlocal diffusion, we can formulate a strong maximum principle for nonlinearities satisfying a geometric condition related to the flux operator of the equation. In our formulation of the strong maximum principle, we find a physical re-interpretation and generalization of the standard PDE conclusion of the principle: we replace constant solutions with solutions of zero flux. We also consider nonlinearities outside the scope of our principle. For highly degenerate conductivities, we demonstrate the invalidity of the strong maximum principle. We also consider intermediate, inconclusive examples, and provide numerical evidence that the strong maximum principle is valid. This suggests that our geometric condition is sharp. nonlocal diffusion nonlinear diffusion integro-differential equations maximum principle strong maximum principle degenerate Mathematics Ravi Shankar verfasserin aut In Axioms MDPI AG, 2012 12(2023), 11, p 1059 (DE-627)718622030 (DE-600)2661511-3 20751680 nnns volume:12 year:2023 number:11, p 1059 https://doi.org/10.3390/axioms12111059 kostenfrei https://doaj.org/article/46bd3234c59e40fb98fbb85ba6c95d98 kostenfrei https://www.mdpi.com/2075-1680/12/11/1059 kostenfrei https://doaj.org/toc/2075-1680 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 12 2023 11, p 1059
allfields_unstemmed	10.3390/axioms12111059 doi (DE-627)DOAJ10127534X (DE-599)DOAJ46bd3234c59e40fb98fbb85ba6c95d98 DE-627 ger DE-627 rakwb eng QA1-939 Tucker Hartland verfasserin aut A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We consider a class of nonlinear integro-differential equations that model degenerate nonlocal diffusion. We investigate whether the strong maximum principle is valid for this nonlocal equation. For degenerate parabolic PDEs, the strong maximum principle is not valid. In contrast, for nonlocal diffusion, we can formulate a strong maximum principle for nonlinearities satisfying a geometric condition related to the flux operator of the equation. In our formulation of the strong maximum principle, we find a physical re-interpretation and generalization of the standard PDE conclusion of the principle: we replace constant solutions with solutions of zero flux. We also consider nonlinearities outside the scope of our principle. For highly degenerate conductivities, we demonstrate the invalidity of the strong maximum principle. We also consider intermediate, inconclusive examples, and provide numerical evidence that the strong maximum principle is valid. This suggests that our geometric condition is sharp. nonlocal diffusion nonlinear diffusion integro-differential equations maximum principle strong maximum principle degenerate Mathematics Ravi Shankar verfasserin aut In Axioms MDPI AG, 2012 12(2023), 11, p 1059 (DE-627)718622030 (DE-600)2661511-3 20751680 nnns volume:12 year:2023 number:11, p 1059 https://doi.org/10.3390/axioms12111059 kostenfrei https://doaj.org/article/46bd3234c59e40fb98fbb85ba6c95d98 kostenfrei https://www.mdpi.com/2075-1680/12/11/1059 kostenfrei https://doaj.org/toc/2075-1680 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 12 2023 11, p 1059
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allfieldsSound	10.3390/axioms12111059 doi (DE-627)DOAJ10127534X (DE-599)DOAJ46bd3234c59e40fb98fbb85ba6c95d98 DE-627 ger DE-627 rakwb eng QA1-939 Tucker Hartland verfasserin aut A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We consider a class of nonlinear integro-differential equations that model degenerate nonlocal diffusion. We investigate whether the strong maximum principle is valid for this nonlocal equation. For degenerate parabolic PDEs, the strong maximum principle is not valid. In contrast, for nonlocal diffusion, we can formulate a strong maximum principle for nonlinearities satisfying a geometric condition related to the flux operator of the equation. In our formulation of the strong maximum principle, we find a physical re-interpretation and generalization of the standard PDE conclusion of the principle: we replace constant solutions with solutions of zero flux. We also consider nonlinearities outside the scope of our principle. For highly degenerate conductivities, we demonstrate the invalidity of the strong maximum principle. We also consider intermediate, inconclusive examples, and provide numerical evidence that the strong maximum principle is valid. This suggests that our geometric condition is sharp. nonlocal diffusion nonlinear diffusion integro-differential equations maximum principle strong maximum principle degenerate Mathematics Ravi Shankar verfasserin aut In Axioms MDPI AG, 2012 12(2023), 11, p 1059 (DE-627)718622030 (DE-600)2661511-3 20751680 nnns volume:12 year:2023 number:11, p 1059 https://doi.org/10.3390/axioms12111059 kostenfrei https://doaj.org/article/46bd3234c59e40fb98fbb85ba6c95d98 kostenfrei https://www.mdpi.com/2075-1680/12/11/1059 kostenfrei https://doaj.org/toc/2075-1680 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 12 2023 11, p 1059
language	English
source	In Axioms 12(2023), 11, p 1059 volume:12 year:2023 number:11, p 1059
sourceStr	In Axioms 12(2023), 11, p 1059 volume:12 year:2023 number:11, p 1059
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topic_facet	nonlocal diffusion nonlinear diffusion integro-differential equations maximum principle strong maximum principle degenerate Mathematics
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authorswithroles_txt_mv	Tucker Hartland @@aut@@ Ravi Shankar @@aut@@
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callnumber-first	Q - Science
author	Tucker Hartland
spellingShingle	Tucker Hartland misc QA1-939 misc nonlocal diffusion misc nonlinear diffusion misc integro-differential equations misc maximum principle misc strong maximum principle misc degenerate misc Mathematics A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations
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topic_title	QA1-939 A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations nonlocal diffusion nonlinear diffusion integro-differential equations maximum principle strong maximum principle degenerate
topic	misc QA1-939 misc nonlocal diffusion misc nonlinear diffusion misc integro-differential equations misc maximum principle misc strong maximum principle misc degenerate misc Mathematics
topic_unstemmed	misc QA1-939 misc nonlocal diffusion misc nonlinear diffusion misc integro-differential equations misc maximum principle misc strong maximum principle misc degenerate misc Mathematics
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title	A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations
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title_full	A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations
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title_sort	strong maximum principle for nonlinear nonlocal diffusion equations
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title_auth	A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations
abstract	We consider a class of nonlinear integro-differential equations that model degenerate nonlocal diffusion. We investigate whether the strong maximum principle is valid for this nonlocal equation. For degenerate parabolic PDEs, the strong maximum principle is not valid. In contrast, for nonlocal diffusion, we can formulate a strong maximum principle for nonlinearities satisfying a geometric condition related to the flux operator of the equation. In our formulation of the strong maximum principle, we find a physical re-interpretation and generalization of the standard PDE conclusion of the principle: we replace constant solutions with solutions of zero flux. We also consider nonlinearities outside the scope of our principle. For highly degenerate conductivities, we demonstrate the invalidity of the strong maximum principle. We also consider intermediate, inconclusive examples, and provide numerical evidence that the strong maximum principle is valid. This suggests that our geometric condition is sharp.
abstractGer	We consider a class of nonlinear integro-differential equations that model degenerate nonlocal diffusion. We investigate whether the strong maximum principle is valid for this nonlocal equation. For degenerate parabolic PDEs, the strong maximum principle is not valid. In contrast, for nonlocal diffusion, we can formulate a strong maximum principle for nonlinearities satisfying a geometric condition related to the flux operator of the equation. In our formulation of the strong maximum principle, we find a physical re-interpretation and generalization of the standard PDE conclusion of the principle: we replace constant solutions with solutions of zero flux. We also consider nonlinearities outside the scope of our principle. For highly degenerate conductivities, we demonstrate the invalidity of the strong maximum principle. We also consider intermediate, inconclusive examples, and provide numerical evidence that the strong maximum principle is valid. This suggests that our geometric condition is sharp.
abstract_unstemmed	We consider a class of nonlinear integro-differential equations that model degenerate nonlocal diffusion. We investigate whether the strong maximum principle is valid for this nonlocal equation. For degenerate parabolic PDEs, the strong maximum principle is not valid. In contrast, for nonlocal diffusion, we can formulate a strong maximum principle for nonlinearities satisfying a geometric condition related to the flux operator of the equation. In our formulation of the strong maximum principle, we find a physical re-interpretation and generalization of the standard PDE conclusion of the principle: we replace constant solutions with solutions of zero flux. We also consider nonlinearities outside the scope of our principle. For highly degenerate conductivities, we demonstrate the invalidity of the strong maximum principle. We also consider intermediate, inconclusive examples, and provide numerical evidence that the strong maximum principle is valid. This suggests that our geometric condition is sharp.
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title_short	A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations
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up_date	2024-07-03T19:43:42.593Z
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A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations

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