Comparison Principle for Weakly Coupled Cooperative Parabolic Systems with Delays

In this article, the validity of the comparison principle (CP) for weakly coupled quasi-linear cooperative systems with delays is proven. This is a powerful tool for studying the qualitative properties of the solutions. The CP is crucial in the proofs of the existence and uniqueness of weak solution...

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Main Author: Georgi Boyadzhiev
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/8/1230
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author Georgi Boyadzhiev
author_facet Georgi Boyadzhiev
author_sort Georgi Boyadzhiev
collection DOAJ
description In this article, the validity of the comparison principle (CP) for weakly coupled quasi-linear cooperative systems with delays is proven. This is a powerful tool for studying the qualitative properties of the solutions. The CP is crucial in the proofs of the existence and uniqueness of weak solutions to cooperative reaction–diffusion systems presented here. Other direct consequences of the CP are the stability of the solution, the attenuation of long time periods, etc. An example model is given by spatial SEIR models with delays. They are suitable for modeling disease spread in space and time and can be described using a weakly coupled cooperative reaction–diffusion system. In this paper, spatial SEIR models with delays are considered in a continuous space. The emphasis is on the qualitative properties of the solutions, which are important for providing a mathematical basis for the model.
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spelling doaj-art-3e4a20d1599b4744866b69a6ff9c433d2025-08-20T02:28:15ZengMDPI AGMathematics2227-73902025-04-01138123010.3390/math13081230Comparison Principle for Weakly Coupled Cooperative Parabolic Systems with DelaysGeorgi Boyadzhiev0Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. G.Bonchev St., 1113 Sofia, BulgariaIn this article, the validity of the comparison principle (CP) for weakly coupled quasi-linear cooperative systems with delays is proven. This is a powerful tool for studying the qualitative properties of the solutions. The CP is crucial in the proofs of the existence and uniqueness of weak solutions to cooperative reaction–diffusion systems presented here. Other direct consequences of the CP are the stability of the solution, the attenuation of long time periods, etc. An example model is given by spatial SEIR models with delays. They are suitable for modeling disease spread in space and time and can be described using a weakly coupled cooperative reaction–diffusion system. In this paper, spatial SEIR models with delays are considered in a continuous space. The emphasis is on the qualitative properties of the solutions, which are important for providing a mathematical basis for the model.https://www.mdpi.com/2227-7390/13/8/1230comparison principleparabolic systemsdelaysspatial SEIR model
spellingShingle Georgi Boyadzhiev
Comparison Principle for Weakly Coupled Cooperative Parabolic Systems with Delays
Mathematics
comparison principle
parabolic systems
delays
spatial SEIR model
title Comparison Principle for Weakly Coupled Cooperative Parabolic Systems with Delays
title_full Comparison Principle for Weakly Coupled Cooperative Parabolic Systems with Delays
title_fullStr Comparison Principle for Weakly Coupled Cooperative Parabolic Systems with Delays
title_full_unstemmed Comparison Principle for Weakly Coupled Cooperative Parabolic Systems with Delays
title_short Comparison Principle for Weakly Coupled Cooperative Parabolic Systems with Delays
title_sort comparison principle for weakly coupled cooperative parabolic systems with delays
topic comparison principle
parabolic systems
delays
spatial SEIR model
url https://www.mdpi.com/2227-7390/13/8/1230
work_keys_str_mv AT georgiboyadzhiev comparisonprincipleforweaklycoupledcooperativeparabolicsystemswithdelays