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Main Authors: Khalil, Kamal, Ndzoumbou, Irmand Leblond Mikiela
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2409.14187
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author Khalil, Kamal
Ndzoumbou, Irmand Leblond Mikiela
author_facet Khalil, Kamal
Ndzoumbou, Irmand Leblond Mikiela
contents In this work, we introduce a compartmental advection-diffusion network model to describe the propagation of stress in a population situated in two interconnected spatial zones during a disaster situation. The model accounts for interactions enabled by intrinsic transitions and imitations within each zone, as well as migrations between these zones. Using semigroup theory and abstract evolution equations, we prove the local existence, uniqueness, and regularity of the solutions. Additionally, we establish the positivity and $L^1$--boundedness of the solutions. Various numerical simulations are provided to illustrate different stress propagation scenarios, including the implementation of a local control strategy designed to minimize stress levels in a population facing a low-risk culture during a dangerous situation.
format Preprint
id arxiv_https___arxiv_org_abs_2409_14187
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle An advection-diffusion-reaction model for stress propagation between two interconnected zones
Khalil, Kamal
Ndzoumbou, Irmand Leblond Mikiela
Analysis of PDEs
34G20, 47D06
In this work, we introduce a compartmental advection-diffusion network model to describe the propagation of stress in a population situated in two interconnected spatial zones during a disaster situation. The model accounts for interactions enabled by intrinsic transitions and imitations within each zone, as well as migrations between these zones. Using semigroup theory and abstract evolution equations, we prove the local existence, uniqueness, and regularity of the solutions. Additionally, we establish the positivity and $L^1$--boundedness of the solutions. Various numerical simulations are provided to illustrate different stress propagation scenarios, including the implementation of a local control strategy designed to minimize stress levels in a population facing a low-risk culture during a dangerous situation.
title An advection-diffusion-reaction model for stress propagation between two interconnected zones
topic Analysis of PDEs
34G20, 47D06
url https://arxiv.org/abs/2409.14187