Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator by Nguyen Dinh Binh

“…The obtained results seem to be optimal and, in particular, improve and extend some recent results on pullback attractors for reaction-diffusion equations in bounded domains.…”
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Dynamics of a Diffusive Predator-Prey Model with Allee Effect on Predator by Xiaoqin Wang, Yongli Cai, Huihai Ma

“…The reaction-diffusion Holling-Tanner prey-predator model considering the Allee effect on predator, under zero-flux boundary conditions, is discussed. …”
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Traveling Wave Solution in a Diffusive Predator-Prey System with Holling Type-IV Functional Response by Deniu Yang, Lihan Liu, Hongyong Wang

“…We establish the existence of traveling wave solution for a reaction-diffusion predator-prey system with Holling type-IV functional response. …”
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Analyzing Similarity Solution of Modified Fisher Equation by Esen Hanaç Duruk, Mehmet Emir Koksal, Ram Jiwari

“…In this paper, we first examine the type of structure of the solutions to the modified form of a nonlinear Fisher’s reaction-diffusion equation. The existence of the traveling wave solution to the equation in the long term is observed by using dynamical system theory and exhibiting a phase space analysis of its stable points. …”
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A Meshfree Method for Numerical Solution of Nonhomogeneous Time-Dependent Problems by Ziwu Jiang, Lingde Su, Tongsong Jiang

“…We propose a new numerical meshfree scheme to solve time-dependent problems with variable coefficient governed by telegraph and wave equations which are more suitable than ordinary diffusion equations in modelling reaction diffusion for such branches of sciences. Finite difference method is adopted to deal with time variable and its derivative, and radial basis functions method is developed for spatial discretization. …”
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Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption by Yulan Wang, Zhaoyin Xiang, Jinsong Hu

“…We investigate a nonlocal reaction diffusion equation with absorption under Neumann boundary. …”
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Internal eradicability for an epidemiological model with diffusion by Sebastian Aniţa, Bedreddine Ainseba

“…Using the framework of nonlinear reaction-diffusion equations, and spectral theory of linear differential operators, we give necessary conditions and sufficient conditions of eradicability.…”
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Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics by Robert Artebrant

“…We study Hopf bifurcation solutions to the Monodomain model equipped with FitzHugh-Nagumo cell dynamics. This reaction-diffusion system plays an important role in the field of electrocardiology as a tractable mathematical model of the electrical activity in the human heart. …”
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Existence of Traveling Wave Solutions for Cholera Model by Tianran Zhang, Qingming Gou, Xiaoli Wang

“…To investigate the spreading speed of cholera, Codeço’s cholera model (2001) is developed by a reaction-diffusion model that incorporates both indirect environment-to-human and direct human-to-human transmissions and the pathogen diffusion. …”
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Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction Term by Jingjing Cai

“…We study a free boundary problem for a reaction diffusion equation modeling the spreading of a biological or chemical species. …”
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Control of Chaotic Calcium Oscillations in Biological Cells by Quanbao Ji, Min Ye

“…The contribution of this present paper is to propose a method that combines a chemical Brusselator reaction-diffusion system with a biological cell system via gap junction for controlling and visualizing the frequency and magnitude of chaotic intracellular calcium oscillations in two cell types, including nonexcitable cells and the glial cells. …”
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Computational Modelling of Thermal Stability in a Reactive Slab with Reactant Consumption by O. D. Makinde

“…The nonlinear partial differential equation governing the transient reaction-diffusion problem is solved numerically using a semidiscretization finite difference technique. …”
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Dynamic Analysis on a Diffusive Two-Enterprise Interaction Model with Two Delays by Yanxia Zhang, Long Li

“…Therefore, it is necessary to investigate the dynamic behavior of reaction-diffusion systems with time delays. In this study, a two-enterprise interaction model with diffusion and delay effects is considered. …”
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Stability and Coexistence of a Diffusive Predator-Prey System with Nonmonotonic Functional Response and Fear Effect by Xiaozhou Feng, Hao Sun, Yangfan Xiao, Feng Xiao

“…Finally, the existence and nonexistence of nonconstant positive steady states of this reaction-diffusion system are established by the Leray–Schauder degree theory and Poincaré inequality.…”
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Global Existence and Blowup Analysis to Single-Species Bacillus System with Free Boundary by Zhi Ling, Zhigui Lin

“…This paper is concerned with a reaction-diffusion equation which describes the dynamics of single bacillus population with free boundary. …”
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Analysis of Wave Solutions of an Adhenovirus-Tumor Cell System by Baba Issa Camara, Houda Mokrani

“…We discuss biological background and mathematical analysis of glioma gene therapy for contributing to cancer treatment. By a reaction-diffusion system, we model interactions between gliom cells and viruses. …”
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Turing patterns in a networked vegetation model by Xiaomei Bao, Canrong Tian

“…A vegetation model composed of water and plants was proposed by introducing a weighted graph Laplacian operator into the reaction-diffusion dynamics. We showed the global existence and uniqueness of the solution via monotone iterative sequence. …”
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The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical System by Yongjun Li, Xiaona Wei, Yanhong Zhang

“…As an application, we obtain the existence of weak D-pullback exponential attractor for reaction diffusion equation in H01 with exponential growth of the external force.…”
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Stability and Hopf Bifurcation in a Three-Component Planktonic Model with Spatial Diffusion and Time Delay by Kejun Zhuang, Gao Jia, Dezhi Liu

“…Due to the different roles that nontoxic phytoplankton and toxin-producing phytoplankton play in the whole aquatic system, a delayed reaction-diffusion planktonic model under homogeneous Neumann boundary condition is investigated theoretically and numerically. …”
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Time Delay In Necrotic Core Formation by Marek Bodnar, Urszula Foryś

“…The model is derived on the basis of reaction-diffusion dynamicsand mass conservation law. We introduce time delay in a cell proliferationprocess. …”
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