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1.
In this paper the singularly perturbed initial boundary value problems for the nonlocal reactiondiffusion system are considered.Using the iteration method and the comparison theorem,the existence and itsasymptotic behavior of the solution for the problem are studied.  相似文献   

2.
This paper is devoted to the study of the regularity of solutions to some systems of reaction–diffusion equations, with reaction terms having a subquadratic growth. We show the global boundedness and regularity of solutions, without smallness assumptions, in any dimension N. The proof is based on blow-up techniques. The natural entropy of the system plays a crucial role in the analysis. It allows us to use of De Giorgi type methods introduced for elliptic regularity with rough coefficients. In spite these systems are entropy supercritical, it is possible to control the hypothetical blow-ups, in the critical scaling, via a very weak norm. Analogies with the Navier–Stokes equation are briefly discussed in the introduction.  相似文献   

3.
郭微 《应用数学》2007,20(2):286-291
就一类具有部分单调性的时滞扩散方程组,我们证明了其行波解的存在性.所采用的方法是通过该系统的适当上、下解构造了Banach空间中的闭凸子集,然后应用Schauder不动点定理,证明相关算子在其上存在不动点.作为该结果的一个重要应用,我们考虑一类时滞的捕食与被捕食模型,证明了其行波解的存在性。  相似文献   

4.
In this paper by using upper-lower solution method the critical wave speed of wave front for a simplified mathematical model of Belousov-Zhabotinskii chemical reaction u_t - u_{xx} = u(1 - u - rv) v_t - v_{xx} = -buv is obtained, where 0 < r < 1, b > 0 are known.  相似文献   

5.
In this paper, the existence of travelling wave solution for nonlinear equation wiili non local advection ρ\frac{∂}{∂t}(\frac{u^m}{m}) = \frac{∂²u}{∂x²}-\frac{∂}{∂x}[φ(k∗u)u]+u^nf(u) is studied in the case of m ≥ 1, n ≥ 1. When ε,φ, f, m and n satisfy some determinate conditions, there exists the travelling wave solution.  相似文献   

6.
阳大春  杨鹤  俞森 《应用数学》2006,19(1):7-12
本文建立了两种群时滞合作系统波前解的存在性定理,扩展了单种群生物模型的结论.  相似文献   

7.
In this paper by using upper-lower solution method, under appropriate assumptions on f and g the existence of travelling wave front solutions for the following reaction-diffusion system is proved: {u_t - u_{xx}, = f(u,v) v_t - v_{xx} = g(u, v) As an application, the necessary and sufficient condition of the existence of monotone solutions for the boundary value problem {u" + cu' + u(1 - u- rv) = 0 v" + cv' - buv = 0 u(-∞) = v(+∞) = 0 u(+∞) = v(-∞) = 1 where 0 < r < 1, 0 < b < \frac{1 - r}{r} are known constants and c is unknown constant to be obtained.  相似文献   

8.
半导体物理中的一个两点边值问题   总被引:2,自引:0,他引:2  
本文研究了在半导体流的区域提纯过程中提出的两点边值问题解的存在性,我们用上、下解方法和Sshauder不动点定理证明了如果Q=2A3Re,其中A是表面速率,Re是Reynolds数,则当0 Q 12.68时,该问题有解. 对[1]的结果(0 Q<8.51时,此问题的解存在)进行了重要的改进.  相似文献   

9.
本文主要研究状态依赖时滞非局部扩散方程的波前解,当出生函数单调时,可以得到单调行波解的存在性和非存在性,然后,由先验估计和Ikehara定理,进一步得到临界波前解的渐近性;当出生函数非单调时,通过引进两个辅助拟单调方程,也可以得到相应非拟单调条件下的存在性结果.  相似文献   

10.
一类无穷时滞周期Lotka-Volterra型系统的正周期解   总被引:2,自引:0,他引:2       下载免费PDF全文
该文研究一类无穷时滞周期Lotka Volterra型系统正周期解的存在性.应用Schauder不动 点定理得到了一个比较一般的正周期解存在定理.文献[1,2]中的主要结果被改进和推广.  相似文献   

11.
一类Fisher方程的行波解   总被引:1,自引:0,他引:1       下载免费PDF全文
本文讨论了一类广义Fisher方程,得到了它的多个显式行波解.  相似文献   

12.
The existence of travelling wave with given end points for parabolic system of nonlinear equations is proven. The nonlinear term depends also on a·xct where x is the multidimensional space variable, t—time, c—the speed of the wave and a—the direction of travel.  相似文献   

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