Well-posedness for fractional reaction-diffusion systems with
mass dissipation in RN

J 2025

Well-posedness for fractional reaction-diffusion systems with mass dissipation in RN

NGUYEN, Phuoc-Tai a Bao Quoc TANG

Základní údaje

Originální název

Well-posedness for fractional reaction-diffusion systems with mass dissipation in RN

Autoři

NGUYEN, Phuoc-Tai a Bao Quoc TANG

Vydání

NONLINEARITY, Bristol, IOP Publishing Ltd, 2025, 0951-7715

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Velká Británie a Severní Irsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.600 v roce 2024

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/25:00143379

Organizační jednotka

Přírodovědecká fakulta

DOI

https://doi.org/10.1088/1361-6544/ae1d07

UT WoS

001618316800001

Klíčová slova anglicky

reaction-diffusion systems; fractional diffusion; duality methods; quadratic growth; intermediate sum conditions

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 16. 1. 2026 14:32, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

The global well-posedness of a large class of reaction-diffusion systems with fractional diffusion in the whole space RN is established. The fractional diffusion accounts for the non-local nature of the problem, modelling scenarios where species follow random walks with long jumps or L & eacute;vy flights. The reactions are assumed to preserve the non-negativity of solutions and conserve or, more generally, dissipate the total mass. Even in the case of local diffusion, it is well known that these two natural assumptions alone do not suffice to prevent finite-time blow-up. In this paper, we show that if the nonlinearities grow at most quadratically, then a unique global bounded solution exists regardless of the fractional order of diffusion. This is achieved by proving a regularizing effect of the fractional diffusion operator and combining it with a H & ouml;lder continuity result for non-local, nonhomogeneous parabolic equations. When the nonlinearities are super-quadratic but satisfy certain intermediate sum conditions depending on the fractional order, we establish the global well-posedness by developing duality methods for the fractional diffusion. These results substantially extend the theory of reaction-diffusion systems with mass dissipation to the setting of fractional diffusion and unbounded domains.

Návaznosti

8J23AT032, projekt VaV

Název: Systémy reakce-difúze s nelokální difuzí

Investor: Ministerstvo školství, mládeže a tělovýchovy ČR, Systémy reakce-difúze s nelokální difuzí, Rakousko

Citovat

NGUYEN, Phuoc-Tai a Bao Quoc TANG. Well-posedness for fractional reaction-diffusion systems with mass dissipation in RN. NONLINEARITY. Bristol: IOP Publishing Ltd, 2025, roč. 38, č. 11, s. 1-49. ISSN 0951-7715. Dostupné z: https://doi.org/10.1088/1361-6544/ae1d07.

@article{2547644,
   author = {Nguyen, PhuocandTai and Tang, Bao Quoc},
   article_location = {Bristol},
   article_number = {11},
   doi = {https://doi.org/10.1088/1361-6544/ae1d07},
   keywords = {reaction-diffusion systems; fractional diffusion; duality methods; quadratic growth; intermediate sum conditions},
   language = {eng},
   issn = {0951-7715},
   journal = {NONLINEARITY},
   title = {Well-posedness for fractional reaction-diffusion systems with mass dissipation in RN},
   url = {https://iopscience.iop.org/article/10.1088/1361-6544/ae1d07},
   volume = {38},
   year = {2025}
}

TY  - JOUR
ID  - 2547644
AU  - Nguyen, Phuoc-Tai - Tang, Bao Quoc
PY  - 2025
TI  - Well-posedness for fractional reaction-diffusion systems with mass dissipation in RN
JF  - NONLINEARITY
VL  - 38
IS  - 11
SP  - 1-49
EP  - 1-49
PB  - IOP Publishing Ltd
SN  - 09517715
KW  - reaction-diffusion systems
KW  - fractional diffusion
KW  - duality methods
KW  - quadratic growth
KW  - intermediate sum conditions
UR  - https://iopscience.iop.org/article/10.1088/1361-6544/ae1d07
N2  - The global well-posedness of a large class of reaction-diffusion systems with fractional diffusion in the whole space RN is established. The fractional diffusion accounts for the non-local nature of the problem, modelling scenarios where species follow random walks with long jumps or L & eacute;vy flights. The reactions are assumed to preserve the non-negativity of solutions and conserve or, more generally, dissipate the total mass. Even in the case of local diffusion, it is well known that these two natural assumptions alone do not suffice to prevent finite-time blow-up. In this paper, we show that if the nonlinearities grow at most quadratically, then a unique global bounded solution exists regardless of the fractional order of diffusion. This is achieved by proving a regularizing effect of the fractional diffusion operator and combining it with a H & ouml;lder continuity result for non-local, nonhomogeneous parabolic equations. When the nonlinearities are super-quadratic but satisfy certain intermediate sum conditions depending on the fractional order, we establish the global well-posedness by developing duality methods for the fractional diffusion. These results substantially extend the theory of reaction-diffusion systems with mass dissipation to the setting of fractional diffusion and unbounded domains.
ER  -

NGUYEN, Phuoc-Tai a Bao Quoc TANG. Well-posedness for fractional reaction-diffusion systems with mass dissipation in RN. \textit{NONLINEARITY}. Bristol: IOP Publishing Ltd, 2025, roč.~38, č.~11, s.~1-49. ISSN~0951-7715. Dostupné z: https://doi.org/10.1088/1361-6544/ae1d07.

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