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1.
We consider a reaction-diffusion system which models a fast reversible reaction of type C 1 + C 2?C 3 between mobile reactants inside an isolated vessel. Assuming mass action kinetics, we study the limit when the reaction speed tends to infinity in case of unequal diffusion coefficients and prove convergence of a subsequence of solutions to a weak solution of an appropriate limiting pde-system, where the limiting problem turns out to be of cross-diffusion type. The proof combines the L 2-approach to reaction-diffusion systems having at most quadratic reaction terms with a thorough exploitation of the entropy functional for mass action systems. The limiting cross-diffusion system has unique local strong solutions for sufficiently regular initial data, while uniqueness of weak solutions is in general open but is shown to be valid under restrictions on the diffusivities.  相似文献   

2.
For β ∈ R, the authors consider the evolution system in the unknown variables u and α { ttu+ xxxxu+ xxtα+(β+|| xu||L2^2) xxu=f, ttα- xxα- xxtα- xxtu=0} describing the dynamics of type III thermoelastic extensible beams, where the dissipation is entirely contributed by the second equation ruling the evolution of the thermal displacement α. Under natural boundary conditions, the existence of the global attractor of optimal regularity for the related dynamical system acting on the phase space of weak energy solutions is established.  相似文献   

3.
For β∈ R,the authors consider the evolution system in the unknown variables u and ααttu+αxxxxu+αxxtα-(β+αxu L22)αxxu=f,αttα-αxxα-αxxtα-αxxtu=0 describing the dynamics of type III thermoelastic extensible beams,where the dissipation is entirely contributed by the second equation ruling the evolution of the thermal displacement α.Under natural boundary conditions,the existence of the global attractor of optimal regularity for the related dynamical system acting on the phase space of weak energy solutions is established.  相似文献   

4.
Recently, in M. Conti et al. (2010) [6] and M. Fabrizio et al. (2010) [12], a new theoretical scheme has been developed in order to study equations with memory, the so-called minimal state approach. The aim of this work is to provide the technical body needed to study the asymptotic behavior of semilinear integro-differential equations of hyperbolic type in the novel framework.  相似文献   

5.
Asymptotic pullback dynamics of a typical stochastic reaction-diffusion system, the reversible Schnackenberg equations, with multiplicative white noise is investigated. The robustness of random attractor with respect to the reverse reaction rate as it tends to zero is proved through the uniform pullback absorbing property and the uniform convergence of reversible to non-reversible cocycles. This result means that, even if the reverse reactions would be neglected, the dynamics of this class of stochastic reversible reaction-diffusion systems can still be captured by the random attractor of the non-reversible stochastic raction-diffusion system in a long run.  相似文献   

6.
一类Lotka-Volterra竞争生态系统的周期解   总被引:1,自引:0,他引:1  
李必文 《应用数学》2006,19(1):183-187
讨论一类特殊的n种群LotkaVolterra竞争生态系统的周期解,应用拓扑度理论中的延拓定理和Lyapunov泛函方法,得到了这类系统周期解的存在性和全局渐近稳定性的充分判据.  相似文献   

7.
黄建华 《应用数学》2006,19(3):473-478
本文讨论了一类时滞反应扩散方程整体吸引子的存在性,减弱了徐道义6对非线性项满足全局Lipschitz条件的要求,证明了解算子半群在分数幂空间Cα=C(-r,0,Xα)中存在整体吸引子.  相似文献   

8.
We consider a two-component reaction-diffusion system with a nonlocal reaction term. A necessary condition and a sufficient condition for the internal stabilizability to zero of one of the two components of the solution while preserving the nonnegativity of both components have been established in [6 S. Ani?a , W.-E. Fitzgibbon , and M. Langlais ( 2009 ). Global existence and internal stabilization for a class of predator-prey systems posed on non coincident spatial domains . Discrete Cont. Dynam. Syst. B 11 : 805822 .[Crossref], [Web of Science ®] [Google Scholar]]. In case of stabilizability, a feedback stabilizing control of harvesting type has been indicated. The rate of stabilization (for the indicated feedback control) is given by the principal eigenvalue of a certain non-selfadjoint operator. A large principal eigenvalue leads to a fast stabilization. The first main goal of this article is to approximate this principal eigenvalue. This is done in two steps. First, we investigate the large-time behavior of the solution to a logistic population dynamics with migration, and next we derive as a consequence a method to approximate the principal eigenvalue. The other main goal is to derive a conceptual iterative algorithm to improve the position of the support of the control in order to get a faster stabilization. Our results apply to prey-predator systems.  相似文献   

9.
10.
考虑具有非局部边界条件的半线性强耦合反应扩散方程组的初边值问题.利用上、下解方法和Leray—Schauder不动点定理等,证明问题在适当条件下的光滑解的存在唯一性.  相似文献   

11.
We prove the existence of the global attractor of Sine-Gordon system with Dirichlet boundary condition and show the attractor is the unique steady state when the damping constant and the diffusion constant are sufficiently large.  相似文献   

12.
This paper is concerned with the traveling waves of a reaction-diffusion SIRQ epidemic model with relapse. We find that the existence and nonexistence of traveling waves are determined by the basic reproduction number of the system and the minimal wave speed. This threshold dynamics is proved by Schauder''s fixed-point theorem combining Lyapunov functional with the theory of asymptotic spreading. Moreover, the numerical simulations are provided to illustrate our analytical results and the effect of the relapse is also discussed.  相似文献   

13.
§ 1  IntroductionThe study of nonlinear dynamics is a fascinating problem which is at the very heartofthe understanding ofmany importantproblems ofthe natural sciences.Infinite dimensionaldynamical systems are very important in nonlinear dynamics.For an infinite dimensionaldynamical system,we mainly study the existence and the structure ofthe attractors.Thereare detailed discussions in [1 ] .Itis especially mentioned there thatthe attractors of gradi-ent systems are of simple structure in s…  相似文献   

14.
In this paper, the existence and nonexistence of finite travelling waves (FTWs) for a semilinear degenerate reaction-diffusion system is studied, where 0 < α i < 1, m ij ≥ 0 and ∑ N j =1 m ij > 0, i, j = 1,...,N. Necessary and sufficient conditions on existence and large time behaviours of FTWs of (I) are obtained by using the matrix theory, Schauder's fixed point theorem, and upper and lower solutions method. Received July 3, 1997, Revised June 23, 1999, Accepted March 29, 2000  相似文献   

15.
A five-mode truncation of Navier-Stokes equation for a two-dimensional incompressible fluid on a torus is studied. Its stationary solutions and stability are presented, the existence of attractor and the global stability of the system are discussed. The whole process, which shows a chaos behavior approached through an involved sequence of bifurcations with the changing of Reynolds number, is simulated numerically. Based on numerical simulation results of bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system are revealed.  相似文献   

16.
一类半线性退化反应扩散方程组的有限行波解   总被引:5,自引:0,他引:5  
王术 《数学学报》2003,46(4):733-738
本文考虑一类半线性退化反应扩散方程组有限行波解的存在性与不存在性,以及有限行波解存在的充要条件与大时间行为被获得.  相似文献   

17.
黄建华  路钢 《应用数学》2000,13(4):40-45
本文利用扰动方法,研究了Fitz-Hugh-Ngaumo方程和双稳反应扩散方程在Neuman边值条件下空间离散后的渐近行为,证明了两个格微分方程组的不变区域、吸引集和整体吸引子的存在性,并给出了离散Fitz-Hugh-Ngaumo方程的整体吸引子的Hausdorff维数估计。  相似文献   

18.
In recent years there has been a growing interest on discrete models, see e.g.[1].[2].We consider a reaction diffusion equation which space-independent system is a Hamilton system with one degree of freedom:  相似文献   

19.
In this paper, we propose a new SIV epidemic model with time delay, which also involves both direct and environmental transmissions. For such model, we first introduce the basic reproduction number $\mathscr{R}$ by using the next generation matrix. And then global stability of the equilibria is discussed by means of Lyapunov functionals and LaSalle''s invariance principle for delay differential equations, which shows that the infection-free equilibrium of the system is globally asymptotically stable if $\mathscr{R}<1$ and the epidemic equilibrium of the system is globally asymptotically stable for $\m  相似文献   

20.
Using Lyapunov functionals the global behaviour of the solutions of a reaction-diffusion system modelling chemotaxis is studied for bounded piecewise smooth domains in the plane. Geometric criteria can be given so that this dynamical system tends to a (not necessarily trivial) stationary state.  相似文献   

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