A cross-diffusion system modeling rivaling gangs: Global existence of bounded solutions and FCT stabilization for numerical simulation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489223" target="_blank" >RIV/00216208:11320/24:10489223 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=CpZ93RwjNh" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=CpZ93RwjNh</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0218202524500349" target="_blank" >10.1142/S0218202524500349</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A cross-diffusion system modeling rivaling gangs: Global existence of bounded solutions and FCT stabilization for numerical simulation

Popis výsledku v původním jazyce

In this paper, we study a gang territorial model consisting of two parabolic and two ordinary differential equations, where a taxis-type mechanism models that the two rivaling gangs are repelled by each other&apos;s graffiti. Our main analytical finding shows the existence of global, bounded classical solutions. By making use of quantitative global estimates, we prove that these solutions converge to homogeneous steady states if the initial data are sufficiently small. Moreover, we perform numerical experiments which show that for different choices of parameters, the system may become diffusion- or convection-dominated, where in the former case the solutions converge toward constant steady states while in the latter case nontrivial asymptotic behavior such as segregation is observed. In order to perform these experiments, we apply a nonlinear finite element flux-corrected transport method (FEM-FCT) which is positivity-preserving. Then we treat the nonlinearities in both the system and the proposed nonlinear scheme simultaneously using fixed-point iteration.

Název v anglickém jazyce

A cross-diffusion system modeling rivaling gangs: Global existence of bounded solutions and FCT stabilization for numerical simulation

Popis výsledku anglicky

In this paper, we study a gang territorial model consisting of two parabolic and two ordinary differential equations, where a taxis-type mechanism models that the two rivaling gangs are repelled by each other&apos;s graffiti. Our main analytical finding shows the existence of global, bounded classical solutions. By making use of quantitative global estimates, we prove that these solutions converge to homogeneous steady states if the initial data are sufficiently small. Moreover, we perform numerical experiments which show that for different choices of parameters, the system may become diffusion- or convection-dominated, where in the former case the solutions converge toward constant steady states while in the latter case nontrivial asymptotic behavior such as segregation is observed. In order to perform these experiments, we apply a nonlinear finite element flux-corrected transport method (FEM-FCT) which is positivity-preserving. Then we treat the nonlinearities in both the system and the proposed nonlinear scheme simultaneously using fixed-point iteration.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA22-01591S" target="_blank" >GA22-01591S: Matematická teorie a numerická analýza rovnic vazkých newtonovských stlačitelných tekutin</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematical Models and Methods in Applied Sciences

ISSN

0218-2025

e-ISSN

1793-6314

Svazek periodika

34

Číslo periodika v rámci svazku

09

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

41

Strana od-do

1739-1779

Kód UT WoS článku

001260458100002

EID výsledku v databázi Scopus

2-s2.0-85197907690