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Existence, uniqueness and stability of pyramidal traveling fronts in reaction-diffusion systems

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Science China Mathematics 2016年第10期59卷 1869-1908页

作者： WANG ZhiCheng LI WanTong RUAN ShiGui School of Mathematics and Statistics Lanzhou University Department of Mathematics University of Miami

In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has attracted a lot of attention and many new types of nonplanar traveling waves have been observed for scalar reaction-diffusion equations with various nonlinearities. In this paper, by using the comparison argument and constructing appropriate super- and subsolutions, we study the existence, uniqueness and stability of three- dimensional traveling fronts of pyramidal shape for monotone bistable systems of reaction-diffusion equations in R3. The pyramidal traveling fronts are characterized as either a combination of planar traveling fronts on the lateral surfaces or a combination of two-dimensional V-form waves on the edges of the pyramid. In particular, our results are applicable to some important models in biology, such as Lotk,u-Volterra competition-diffusion systems with or without spatio-temporal delays, and reaction-diffusion systems of multiple obligate mutualists.

关键词： reaction-diffusion systems bistability pyramidal traveling fronts existence uniqueness stability

Entire solutions for some reaction-diffusion systems

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International Journal of Biomathematics 2015年第4期8卷 181-204页

作者： Guangying Lv Dang Luo Institute of Contemporary MathematicsHenan University Kaifeng 575001 P. R. China College of Mathematics and Information SciencesNorth China University of Water Resources and Electric Power Zhengzhou 450011 P. R. China

This paper is concerned with the existence of entire solutions of some reaction-diffusion systems. We first consider Belousov-Zhabotinskii reaction model. Then we study a general model. Using the comparing argument and sub-super-solutions method, we obtain the existence of entire solutions which behave as two wavefronts coming from the both sides of x-axis, where an entire solution is meant by a classical solution defined for all space and time variables. At last, we give some examples to explain our results for the general models.

关键词： reaction-diffusion systems entire solutions traveling wavefronts sub-super-solutions.

On the Motion Law of Fronts for Scalar reaction-diffusion Equations with Equal Depth Multiple-Well Potentials

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Chinese Annals of Mathematics,Series B 2017年第1期38卷 83-148页

作者： Fabrice BETHUEL Didier SMETS UPMC-Paris6 UMR 7598 LJLLParisF-75005France

Slow motion for scalar Allen-Cahn type equation is a well-known phenomenon,precise motion law for the dynamics of fronts having been established first using the socalled geometric approach inspired from central manifold theory(see the results of Carr and Pego in 1989). In this paper, the authors present an alternate approach to recover the motion law, and extend it to the case of multiple wells. This method is based on the localized energy identity, and is therefore, at least conceptually, simpler to implement. It also allows to handle collisions and rough initial data.

关键词： reaction-diffusion systems Parabolic equations Singular limits

On a non-autonomous reaction-convection diffusion model to study the bacteria distribution in a river

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International Journal of Biomathematics 2017年第6期10卷 25-49页

作者： Imene Meriem Mostefaoui Ali Moussaoui Laboratoire de Mathematiques Image et Applications Universite de La Rochelle Pdle Sciences et Technologies Avenue Michel Crepeau 17000 La Rochelle France Laboratoire D'Analyse Non Lineaire et Mathematiques Appliquees Universite de Tlemcen Tlemcen Algeria Laboratoire D'Analyse Non Lineaire et Mathematiques Appliquees Departement de Mathematique Faculte des Sciences Universite de Tlemcen Tlemcen Algeria

In this paper, we propose a non-autonomous convection-reaction diffusion system （CDI） with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant bacteria （ARB） in a river. The main contributions of this paper are：（i） the determination of the limit set of the system by applying the semigroups theory, it is shown that it is reduced to the solutions of the associated elliptic system （CDI）e, （ii） sufficient conditions for the existence of a positive solution of （CDI）e based on the Leray-Schauder＇s degree theory. Numerical simulations which support our theoretical analysis are also given.

关键词： reaction-diffusion systems steady states problems degree theory semi-groups.

一类半线性反应扩散方程组的二层线性化有限差分格式

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高等学校计算数学学报 2008年第3期30卷 250-260页

作者：吴宏伟东南大学数学系

1引言本文考虑下面的半线性反应扩散方程组初边值问题的数值解:

关键词： semilinear reaction-diffusion systems finite difference convergence stability

Global well-posedness of coupled parabolic systems

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Science China Mathematics 2020年第2期63卷 321-356页

作者： Runzhang Xu Wei Lian Yi Niu College of Automation Harbin Engineering UniversityHarbin 150001China College of Science Harbin Engineering UniversityHarbin 150001China The Institute of Mathematical Sciences The Chinese University of Hong KongHong KongChina School of Information Science and Engineering Shandong Normal UniversityJinan 250014China

The initial boundary value problem of a class of reaction-diffusion systems(coupled parabolic systems)with nonlinear coupled source terms is considered in order to classify the initial data for the global existence,finite time blowup and long time decay of the *** whole study is conducted by considering three cases according to initial energy:the low initial energy case,critical initial energy case and high initial energy *** the low initial energy case and critical initial energy case the sufficient initial conditions of global existence,long time decay and finite time blowup are given to show a sharp-like *** addition,for the high initial energy case the possibility of both global existence and finite time blowup is proved first,and then some sufficient initial conditions of finite time blowup and global existence are obtained,respectively.

关键词： reaction-diffusion systems coupled parabolic systems global existence asymptotic behavior finite time blowup

Spiral wave chimeras in populations of oscillators coupled to a slowly varying diffusive environment

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Frontiers of physics 2023年第1期18卷 71-83页

作者： Lei Yang Yuan He Bing-Wei Li School of Physics Hangzhou Normal UniversityHangzhou 311121China

Chimera states are firstly discovered in nonlocally coupled oscillator *** a nonlocal coupling arises typically as oscillators are coupled via an external environment whose characteristic time scaleτis so small(i.e.,τ→0)that it could be eliminated ***,whether the chimera states still exist in the opposite situation(i.e.,τ≫1)is ***,by coupling large populations of Stuart–Landau oscillators to a diffusive environment,we demonstrate that spiral wave chimeras do exist in this oscillator-environment coupling system even whenτis very *** transitions such as from spiral wave chimeras to spiral waves or unstable spiral wave chimeras as functions of the system parameters are explored.A physical picture for explaining the formation of spiral wave chimeras is also *** existence of spiral wave chimeras is further confirmed in ensembles of FitzHugh–Nagumo oscillators with the similar oscillator-environment coupling *** results provide an affirmative answer to the observation of spiral wave chimeras in populations of oscillators mediated via a slowly changing environment and give important hints to generate chimera patterns in both laboratory and realistic chemical or biological systems.

关键词： spiral wave chimeras reaction-diffusion systems oscillator-environment coupling pattern formation

Dynamics of a Mutualistic Model with diffusion

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Analysis in Theory and Applications 2017年第3期33卷 206-218页

作者： Mei Li School of Applied Mathematics Nanjing University of Finance and EconomicsNanjing 210023China

This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by discussing its Jacobian matrix, we give two priori estimates and prove that the model is permanent when ε1 ＋ε2≠ 0. Moreover sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the model are obtained. Nonexistence of nonconstant positive steady states of the model is also given. When ε1 ＋ε2 = 0, grow up property is derived if the geometric mean of the interaction coefficients is greater than I （a1a2 〉 1）, while if the geometric mean of the interaction coefficients is less than I （a1a2 〈 1）, there exists a global solution. Finally, numerical simulations are given.

关键词： reaction-diffusion systems mutualistic model equilibrium permanence grow-up.

Expanding or Static Universe: Emergence of a New Paradigm

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International Journal of Astronomy and Astrophysics 2021年第2期11卷 190-231页

作者： Paul A. LaViolette The Starburst Foundation Niskayuna NY USA

The no-evolution, concordance expanding universe cosmology and no-evolution, static universe tired light model are compared against observational data on eight cosmology tests. The no-evolution tired light model is found to make a superior fit on all tests. Any attempts to introduce evolutionary corrections to improve the concordance cosmology fit on one test often worsen its fit on other tests. Light curve data of high redshift gamma ray bursts and quasars fail to support claims for cosmological time dilation due to expansion. Also, the SCP supernova light curve test results are considered to be flawed by selection effect biases. The big bang theory also has difficulty accounting for redshift quantization, for the multi-megaparsec periodicity seen in the distribution of galaxy superclusters, and for the discovery of galaxies at redshifts as high as z ~11.9. In overview, it is concluded that a static universe cosmology must be sought to explain the origin of the universe. One possible choice is a cosmology that predicts nonconservative tired-light redshifting in intergalactic space, the continuous creation of neutrons in space, the rate of matter creation scaling with both celestial body mass and temperature, galaxies growing progressively in size, and changing their morphology in the manner suggested by Jeans and Hubble.

关键词： Cosmological Redshift Tired Light Effect Hubble Constant Galactic Evolution Continuous Creation Subatomic Particles reaction-diffusion systems Open systems Self-Organizing systems Observational Cosmology Tolman Test Angular-Size-Redshift Test Hubble Diagram Supernovae