Algebro-Geometric Solutions of the Coupled Chaffee-Infante Reaction Diffusion Hierarchy by Chao Yue, Tiecheng Xia

“…The coupled Chaffee-Infante reaction diffusion (CCIRD) hierarchy associated with a 3×3 matrix spectral problem is derived by using two sets of the Lenard recursion gradients. …”
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A reaction-diffusion system modeling the spread of resistance to an antimalarial drug by Nicolas Bacaër, Cheikh Sokhna

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Continuous Dependence in Front Propagation for Convective Reaction-Diffusion Models with Aggregative Movements by Luisa Malaguti, Cristina Marcelli, Serena Matucci

“…The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. …”
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Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion Model by Lili Meng, Yutao Han, Zhiyi Lu, Guang Zhang

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Spatiotemporal Patterns in a Ratio-Dependent Food Chain Model with Reaction-Diffusion by Lei Zhang

“…Our results show that reaction-diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics. …”
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Anticollocated Backstepping Observer Design for a Class of Coupled Reaction-Diffusion PDEs by Antonello Baccoli, Alessandro Pisano

“…The state observation problem is tackled for a system of n coupled reaction-diffusion PDEs, possessing the same diffusivity parameter and equipped with boundary sensing devices. …”
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A Nonoscillatory Second-Order Time-Stepping Procedure for Reaction-Diffusion Equations by Philku Lee, George V. Popescu, Seongjai Kim

“…After a theory of morphogenesis in chemical cells was introduced in the 1950s, much attention had been devoted to the numerical solution of reaction-diffusion (RD) partial differential equations (PDEs). …”
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Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation by Ming Mei, Yau Shu Wong

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Adaptive Extraction of Oil Painting Texture Features Based on Reaction Diffusion Equation by Qicai Huang

“…Inspired by the restoration and decomposition functional model of equal oil painting, we propose a reaction diffusion equation model. The new model contains two reaction diffusion equations with different principal parts. …”
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Exponential Stability of Coupled Systems on Networks with Mixed Delays and Reaction-Diffusion Terms by Wenxue Li, Tianrui Chen, Ke Wang

“…This paper is concerned with the stability analysis issue for coupled systems on networks with mixed delays and reaction-diffusion terms (CSNMRs). By employing Lyapunov method and Kirchhoff's Theorem in graph theory, a systematic method is proposed to guarantee exponential stability of CSNMRs. …”
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Numerical Simulation and Symmetry Reduction of a Two-Component Reaction-Diffusion System by Jina Li, Xuehui Ji

“…In this paper, the symmetry classification and symmetry reduction of a two-component reaction-diffusion system are investigated, the reaction-diffusion system can be reduced to system of ordinary differential equations, and the solutions and numerical simulation will be showed by examples.…”
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Stability of Stochastic Reaction-Diffusion Recurrent Neural Networks with Unbounded Distributed Delays by Chuangxia Huang, Xinsong Yang, Yigang He, Lehua Huang

“…Stability of reaction-diffusion recurrent neural networks (RNNs) with continuously distributed delays and stochastic influence are considered. …”
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Green’s Functions on Various Time Scales for the Time-Fractional Reaction-Diffusion Equation by Alexey Zhokh, Peter Strizhak

“…Based on the developed Green’s functions, the exact analytic asymptotic solutions of the time-fractional reaction-diffusion equation are obtained. The applicability of the obtained solutions is demonstrated via quantification of the reaction-diffusion kinetics during heterogeneous catalytic chitin conversion to chitosan.…”
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Global Asymptotic Stability in a Class of Reaction-Diffusion Equations with Time Delay by Yueding Yuan, Zhiming Guo

“…We study a very general class of delayed reaction-diffusion equations in which the reaction term can be nonmonotone and spatially nonlocal. …”
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Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model by Guangrui Li, Ming Mei, Yau Shu Wong

“…The paper is devoted to the study of a time-delayed reaction-diffusion equation of age-structured single species population. …”
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An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems by Chichia Chiu, Jui-Ling Yu

“…Reaction-diffusion-chemotaxis systems have proven to be fairlyaccurate mathematical models for many pattern formation problems in chemistryand biology. …”
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Upper semicontinuity of the attractor for lattice dynamical systems of partly dissipative reaction diffusion systems by Ahmed Y. Abdallah

“…We investigate the existence of a global attractor and its upper semicontinuity for the infinite-dimensional lattice dynamical system of a partly dissipative reaction diffusion system in the Hilbert space l2×l2. Such a system is similar to the discretized FitzHugh-Nagumo system in neurobiology, which is an adequate justification for its study.…”
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Conservation Laws and Exact Solutions for a Reaction-Diffusion Equation with a Variable Coefficient by Zhijie Cao, Yiping Lin

“…In this paper a variable-coefficient reaction-diffusion equation is studied. We classify the equation into three kinds by different restraints imposed on the variable coefficient b(x) in the process of solving the determining equations of Lie groups. …”
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Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model by Xiaoqin Wang, Yongli Cai

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Lower Bound for the Blow-Up Time for the Nonlinear Reaction-Diffusion System in High Dimensions by Baiping Ouyang, Wei Fan, Yiwu Lin

“…In this paper, we study the blow-up phenomenon for a nonlinear reaction-diffusion system with time-dependent coefficients under nonlinear boundary conditions. …”
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