Self-Similar Solutions for a Class of Reaction-Diffusion Systems

The self similar solutions for a class of reaction diffusion systems are analyzed. The existence and qualitative properties are discussed.

Global Bounded Solutions for Reaction-diffusion Systems with a Full Matrix of Diffusion Coefficients and a Balance Law

This paper deals with an initial boundary value problem for the strongly coupledreaction-diffusion systems with a full matrix of diffusion coefficients. The global existence ofsolutions is proved by using the techniques based on invariant regions, Lyapunov functionalmethods, and local Lp prior estimates independent of time.

Global attractors associated with general partly dissipative reaction-diffusion systems in unbounded domains

The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .

Research on Policy Diffusion Path and Reproduction of River Chief System

The River Chief System (RCS) has evolved from local innovative practices to a national water governance strategy to address the current challenges in China’s water environmental management. In contrast to existing research that focuses on the strengths, weaknesses, and improvements of RCS, this study uses literature study to reveal the dynamic evolution of RCS through three phases, with RCS spreading from developed coastal areas to central and western inland regions. RCS’s diffusion path involves vertical diffusion between central and local levels and horizontal diffusion among local governments. Moreover, RCS has also achieved conceptual spillover, gradually expanding into other governance domains, such as the Lake Chief System, the Field Chief System, the Forestry Chief System, and the integration of multiple chief roles. However, it is essential to scrutinize the phenomenon of applying similar governance mechanisms to different areas, as it may result in challenges such as overburdening local governments, insufficient public participation, oversimplification of differences in natural resource endowments, and limited applicability. This study also provides suggestions on how to address these challenges. The study contributes theoretical insights and policy implications, providing a foundation for practical policy innovation.

Analysis of diffusion-adsorption equivalency of landfill liner systems for organic contaminants

The equivalence between multilayered barriers regarding diffusion and adsorption was studied. The bottom boundary of the liner system is defined by assuming concentration continuous and flux continuous conditions of the contaminant between the bottom liner layer and the underlying soil. Five different liner systems were compared in terms of solute breakthrough time. The results of the analysis showed that breakthrough time of the hydrophobic organic compounds for a 2-meter-thick compacted clay liner （CCL） could be 3-4 orders of magnitude is greater than the breakthrough time for a geosynthetic clay liner （GCL） composite liner. The GM/GCL and GM/CCL composite liner systems provide a better diffusion barrier for the hydrophilic organic compounds than that for the hydrophobic compounds due to their different Henry＇s coefficient. The calculated breakthrough times of the organic contaminants for the Chinese standard liner systems were found to be generally greater than those for the GCL alternatives, for the specific conditions examined. If the distribution coefficient increases to 2.8 for the hydrophobic compounds or 1.0 for the hydrophilic compounds, the thickness of the attenuation layer needed to achieve the same breakthrough time as the standard liner systems can be reduced by a factor of about 1.9-2.4. As far as diffusive and adsorption contaminant transport are concerned, GM or GCL is less effective than CCL.

A Class of Nonlinear Nonlocal Singularly Perturbed Reaction Diffusion Systems

The singularly perturbed initial boundary value problems for the reaction diffusion system are raised. Firstly, under suitable conditions, using a iteration technique, the differential inequalities theorem is constructed and introducing two auxiliary functions the existence and uniqueness theorem of solution for the basic reaction diffusion system is proved. Using the singularly perturbed method the formal asymptotic expressions of the solution are constructed with power series theory. By using the comparison theorem the existence and its asymptotic behavior of solution for the original problem are studied. Finally, using method of estimate inequalities, the structure of solutions for the problem is discussed thoroughly in three cases and asymptotic solution of the original problem is given. The asymptotic behavior of solution in the three cases is proved.

EXISTENCE OF SOLUTIONS FOR GRADIENT SYSTEMS WITH APPLICATION TO DIFFUSION PROBLEMS INVOLVING NONCONVEX ENERGIES

In this paper, we establish the existence of solutions for gradient systems ofevolution under some type （M） and semi-coerciveness conditions. The main result is appliedin order to solve nonlinear diffusion equations involving nonconvex energies.

Critical Fujita Exponents for Localized Reaction Diffusion Systems

In this paper, we prove the existence of cirtical Fujita exponents for a class of localized reaction diffusion systems.

Dynamics Behaviors of a Reaction-Diffusion Predator-Prey System with Beddington-DeAngelis Functional Response and Delay

This paper is concerned with the existence of traveling wave solutions in a reaction-diffusion predator-prey system with Beddington-DeAngelis functional response and a discrete time delay. By introducing a partial quasi-monotonicity condition and constructing a pair of upper-lower solutions, we establish the existence of traveling wave solutions. Moreover, a numerical simulation is carried out to illustrate the theoretical results.

EXACT SOLUTIONS A COUPLED NONLINEAR REACTION-DIFFUSION SYSTEM

In this paper we shall present, certain type of exact solutions for a coupled partial differential equation by using hyperbolic tangent method.

NONTRIVIAL SOLUTIONS OF COMPETITIVE-DIFFUSIVE SYSTEMS WITH SMALL DIFFUSION

We discuss nontrivial steady-state solutions of a competitive-diffusive systems with small diffusion in which two interacting species u and v inhibit the same bounded region. By using methods of bifurcation theory and indefinite weight function, we prove the existence and uniqueness of solutions which are positive in both u and v and asymptotically stable corresponding to the case where the populations can co-exist.

MapReduce based computation of the diffusion method in recommender systems

The performance of existing diffusion-based algorithms in recommender systems is still limited by the processing ability of a single computer. In order to conduct the diffusion computation on large data sets,a parallel implementation of the classic diffusion method on the MapReduce framework is proposed. At first,the diffusion computation is transformed from a summation format to a cascade matrix multiplication format,and then,a parallel matrix multiplication algorithm based on dynamic vector is proposed to reduce the CPU and I / O cost on the MapReduce framework,which can also be applied to other parallel matrix multiplication scenarios. Then,block partitioning is used to further improve the performance,while the order of matrix multiplication is also taken into consideration.Experiments on different kinds of data sets have verified the efficiency of the proposed method.

NONTRIVIAL EQUILIBRIUM SOLUTIONS FOR A SEMILINEAR REACTION-DIFFUSION SYSTEM

By the degree theory on positive cone together with the technique of a priori estimate, the nontrivial equilibrium solutions of a strong nonlinearity and weak coupling reaction diffusion system and the structure of the equilibrium solutions are discussed.

Stationary patterns in a discrete bistable reaction-diffusion system:mode analysis

This paper theoretically analyses and studies stationary patterns in diffusively coupled bistable elements. Since these stationary patterns consist of two types of stationary mode structure： kink and pulse, a mode analysis method is proposed to approximate the solutions of these localized basic modes and to analyse their stabilities. Using this method, it reconstructs the whole stationary patterns. The cellular mode structures （kink and pulse） in bistable media fundamentally differ from stationary patterns in monostable media showing spatial periodicity induced by a diffusive Taring bifurcation.

A Class of Singularly Perturbed Problems for Nonlinear Two-Species Competitive Reaction-Diffusion System

A class of nonlinear two-species competitive singularly perturbed initial-boundary-value problems for reaction-diffusion systems are studied. Under suitable assumptions, by using the stretched variable, the formal asymptotic expansion for the problems is constructed. The uniform validity of the solution for initial-boundary-value problems is obtained by using the theory of differential inequalities.

Relation between the complex Ginzburg-Landau equation and reaction-diffusion system

The complex Ginzburg-Landau equation （CGLE） has been used to describe the travelling wave behaviour in reaction-diffusion （RD） systems. We argue that this description is valid only when the RD system is close to the Hopf bifurcation, and is not valid when a RD system is away from the onset. To test this, we study spirals and anti-spirals in the chlorite-iodide-malonic acid （CIMA） reaction and the corresponding OGLE. Numerical simulations confirm that the OGLE can only be applied to the CIMA reaction when it is very near the Hopf onset.

PERIODIC SOLUTIONS FOR GENERALIZED PREDATOR-PREY SYSTEMS WITH TIME DELAY AND DIFFUSION

A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion systemwhere ai(t),bi(t) and Di(t)(i = 1, 2) axe positive continuous T-periodic functions, gi(t,xi) (i = 1,2) and h(t,y) are continuous and T-periodic with respect to t and h(t,y) > 0 for y>0,t, y∈R,pi(x)(i=1,2) are continuous and monotonously increasing functions, and Pi(xi)>0 for xi>0.

Global existence and blow-up of solutions to reaction-diffusion system with a weighted nonlocal source

In this paper,we study a semi-linear reaction-diffusion system with a weighted nonlocal source,subject to the null Dirichlet boundary condition.Under certain conditions,we prove that the classical solution exists globally and blows up in finite time respectively,and then obtain the uniform blow-up rate in the interior.

Uniqueness of solution of a quasi-linear Reaction-diffusion system

In this paper,we consider nonnegative classical solutions of a Quasi-linear reaction-diffusion system with nonlinear boundary conditions.We prove the uniqueness of a nonnegative classical solution to this problem.

GLOBAL EXISTENCE OF SOLUTIONS FOR A STRONGLY COUPLED REACTION-DIFFUSION SYSTEM

This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global existence and uniqueness of a. smooth. solution for this IBVP under some appropriate conditions.