Global Existence and Asymptotic Behavior for a Reaction–Diffusion System with Unbounded Coefficients

Mohamed Majdoub; Nasser Eddine Tatar

doi:10.1007/s00009-023-02394-2

Global Existence and Asymptotic Behavior for a Reaction–Diffusion System with Unbounded Coefficients

Mohamed Majdoub^*, Nasser Eddine Tatar

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a reaction–diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction–diffusion equations with unbounded time-dependent coefficients and different polynomial reaction terms. An exponential decay of the globally bounded solutions is proved. The key tool of the proofs are properties of analytic semigroups and some inequalities.

Original language	English
Article number	189
Journal	Mediterranean Journal of Mathematics
Volume	20
Issue number	4
DOIs	https://doi.org/10.1007/s00009-023-02394-2
State	Published - Aug 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

Analytic semi-group
exponential decay
fractional operator
reaction–diffusion system
sectorial operator

ASJC Scopus subject areas

General Mathematics

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10.1007/s00009-023-02394-2

Cite this

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abstract = "We consider a reaction–diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction–diffusion equations with unbounded time-dependent coefficients and different polynomial reaction terms. An exponential decay of the globally bounded solutions is proved. The key tool of the proofs are properties of analytic semigroups and some inequalities.",

keywords = "Analytic semi-group, exponential decay, fractional operator, reaction–diffusion system, sectorial operator",

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AU - Majdoub, Mohamed

AU - Tatar, Nasser Eddine

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Y1 - 2023/8

N2 - We consider a reaction–diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction–diffusion equations with unbounded time-dependent coefficients and different polynomial reaction terms. An exponential decay of the globally bounded solutions is proved. The key tool of the proofs are properties of analytic semigroups and some inequalities.

AB - We consider a reaction–diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction–diffusion equations with unbounded time-dependent coefficients and different polynomial reaction terms. An exponential decay of the globally bounded solutions is proved. The key tool of the proofs are properties of analytic semigroups and some inequalities.

KW - Analytic semi-group

KW - exponential decay

KW - fractional operator

KW - reaction–diffusion system

KW - sectorial operator

UR - https://www.scopus.com/pages/publications/85154055920

U2 - 10.1007/s00009-023-02394-2

DO - 10.1007/s00009-023-02394-2

M3 - Article

AN - SCOPUS:85154055920

SN - 1660-5446

VL - 20

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 4

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ER -

Global Existence and Asymptotic Behavior for a Reaction–Diffusion System with Unbounded Coefficients

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this