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We study systems of reaction-diffusion equations perturbed by multiplicative noise, where the reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth. Our results apply to a broad class of…

Probability · Mathematics 2026-05-27 Dionysis Milesis , Michael Salins

The global existence and boundedness of solutions to volume-surface reaction diffusion systems with a mass control condition are investigated. Such systems arise typically in e.g. cell biology, ecology or fluid mechanics, when some…

Analysis of PDEs · Mathematics 2024-12-18 Juan Yang , Bao Quoc Tang

In this work, we study the global existence of solutions for a class of semilinear nonlocal reaction-diffusion systems with $m$ components on a bounded domain $\Omega$ in $\mathbb{R}^n$ with smooth boundary. The initial data is assumed to…

Analysis of PDEs · Mathematics 2025-10-09 Md Shah Alam , Jeff Morgan

We consider combustion problems in the presence of complex chemistry and nonlinear diffusion laws leading to fully nonlinear multispecies reaction-diffusion equations. We establish results of existence of solution and maximum principle,…

Analysis of PDEs · Mathematics 2013-10-11 Martine Marion , Roger Temam

We study the boundedness and convergence to equilibrium of weak solutions to reaction-diffusion systems with nonlinear diffusion. The nonlinear diffusion is of porous medium type and the nonlinear reaction terms are assumed to grow…

Analysis of PDEs · Mathematics 2017-11-09 Klemens Fellner , Evangelos Latos , Bao Quoc Tang

The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing…

Analysis of PDEs · Mathematics 2024-12-17 Laurent Desvillettes , Kim Dang Phung , Bao Quoc Tang

The aim of this paper is to construct invariant regions of a generalized m-component reaction-diffusion system with a tri-diagonal Toeplitz matrix of diffusion coefficients and prove the global existence of solutions using Lyapunov…

Analysis of PDEs · Mathematics 2014-12-09 Salem Abdelmalek

A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…

Analysis of PDEs · Mathematics 2021-02-24 Wenjie Zuo , Junping Shi

A class of coupled time-space fractional reaction-diffusion systems derived from reversible chemical reactions over a bounded domain is investigated. Employing mainly an appropriate Lyapunov functional and an improved maximum principle, we…

Analysis of PDEs · Mathematics 2026-03-04 Redouane Douaifia , Salem Abdelmalek , Mokhtar Kirane

This paper is concerned with the local and global existence of solutions for a generalized $m$-component reaction--diffusion system with a tridiagonal $2$--Toeplitz diffusion matrix and polynomial growth. We derive the eigenvalues and…

Analysis of PDEs · Mathematics 2016-02-09 Salem Abdelmalek , Samir Bendoukha

The goal of this work is to establish the global existence of nonnegative classical solutions in all dimensions for a system of highly nonlinear reaction-diffusion equations. We address the case for different diffusion coefficients and the…

Analysis of PDEs · Mathematics 2022-09-16 Nibedita Ghosh , Hari Shankar Mahato

The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy…

Analysis of PDEs · Mathematics 2021-09-27 Klemens Fellner , Julian Fischer , Michael Kniely , Bao Quoc Tang

We prove a global existence, uniqueness and regularity result for a two-species reaction-diffusion volume-surface system that includes nonlinear bulk diffusion and nonlinear (weak) cross diffusion on the active surface. A key feature is a…

Analysis of PDEs · Mathematics 2019-04-04 Karoline Disser

In this paper we use the homotopy invariants methods to study the global dynamics of the reaction-diffusion systems that are at resonance at infinity. Considering degrees of the resonance for the nonlinear perturbation we establish…

Analysis of PDEs · Mathematics 2020-09-24 Piotr Kokocki

In this work we study global well-posedness and large time behaviour for a typical reaction--diffusion system, which include degenerate diffusion, and whose non-linearities arise from chemical reactions. We show that there is an {\it…

Analysis of PDEs · Mathematics 2020-04-27 Amit Einav , Jeff Morgan , Bao Quoc Tang

The purpose of this paper is to prove global existence of solutions for general systems of reaction diffusion equations with nonlinearities for which only two main proprieties hold: Quasi-Positivity and balance law but with two…

Dynamical Systems · Mathematics 2023-02-07 Said Kouachi

We study global-in-time behavior of the solution to a reaction-diffusion system with mass conservation, as proposed in the study of cell polarity, particularly, the second model of \cite{oi07}. First, we show global-in-time existence of…

Analysis of PDEs · Mathematics 2015-11-13 Evangelos Latos , Yoshihisa Morita , Takashi Suzuki

This paper deals with an Gierer-Meinhardt model, with three substances, formed Reaction-Diffusion system with fractional reaction. To prove global existence for solutions of this system presents difficulties at the boundednees of fractionar…

Analysis of PDEs · Mathematics 2010-07-26 Abdelmalek Salem , Louafi Hichem , Youkana Amar

We study the global existence of classical solutions to volume-surface reaction-diffusion systems with control of mass. Such systems appear naturally from modeling evolution of concentrations or densities appearing both in a volume domain…

Analysis of PDEs · Mathematics 2021-01-21 Jeff Morgan , Bao Quoc Tang

In this paper, we prove global-in-time existence of strong solutions to a class of fractional parabolic reaction-diffusion systems posed in a bounded domain of $\mathbb{R}^N$. The nonlinear reactive terms are assumed to satisfy natural…

Analysis of PDEs · Mathematics 2023-06-07 Maha Daoud , El-Haj Laamri , Azeddine Baalal