带有非局部源和非局部边界条件的抛物型方程组解的爆破性质

考虑带有非局部Dirichlet 边界条件,反应项为非线性非局部源的半线性抛物型方程组解的blow-up性质.首先利用上下解方法建立解整体存在和有限时刻blow-up 的条件, 并给出解的两个分量同时blow-up的必要 条件和充分条件; 最后给出区域内部一致blow-up模式的刻画.     

关于Gray-Scott模型的模式生成

考虑一个著名的椭圆型方程组即Gray-Scott模型,获得了其正解的进一步结果.具体地讲,给出了正解更精细的先验估计,进而,当参数在一定范围内变化时,建立了非常数正解的存在性和不存在性改进性的结论.所得结果导出了判别模式生成的一些确定性条件.     

OSCILLATION AND ASYMPTOTIC BEHAVIOR OF SOME SECOND-ORDER RETARDED DIFFERENTIAL EQUATIONS

In this paper, we consider the following second order retarded differential equations x″(t)+cx′(t)=qx(t-σ)-lx(t-δ) (1) x″(t)+p(t)x(t-τ)=0 (2) We give some sufficient conditions for the oscillation of all solutions of Eq. (1) in the case where q, ι, σ, δ are positive numbers and c is a real number. And also, we study the asymptotic behavior of the nonoscillatory solutions. If necessary, we give some examples to illustrate our results. At last, we study Eq. (2) with some conditions on p(t).     

On the Properties of ParabolicSolutions of Non-localEquations

In this short note, we investigate the properties of positive solutions for some non-local parabolic equations. The conditions on the global existence and blowup in finite time of solution are given.     

带梯度吸收项的快扩散方程的自相似奇性解

研究一类带有非线性梯度吸收项的快速扩散方程的自相似奇性解．通过自相似变换,该自相似奇性解满足一个非线性常微分方程的边值问题,再利用打靶法技巧研究该常微分方程初值问题解的存在唯一性并根据初值的取值范围对其解进行了分类．通过对这些解类的性质的分析研究,得出了自相似强奇性解存在唯一性的充分必要条件,此时自相似奇性解就是强奇性解．     

Diffusion-driven instability and Hopf bifurcation in Brusselator system

The Hopfbifurcation for the Brusselator ordinary-differential-equation （ODE） model and the corresponding partial-differential-equation （PDE） model are investigated by using the Hopf bifurcation theorem. The stability of the Hopf bifurcation periodic solution is discussed by applying the normal form theory and the center manifold theorem. When parameters satisfy some conditions, the spatial homogenous equilibrium solution and the spatial homogenous periodic solution become unstable. Our results show that if parameters are properly chosen, Hopf bifurcation does not occur for the ODE system, but occurs for the PDE system.     

Existence of Global Solutions to a Semilinear Hyperbolic System

LetD:~0'/0t'--bdenotetheD'AlembertianandR; ":=R xR",thenweconsiderthefollowingproblemDa~III',Da~III',(t,X)ERI ",(1)u(0,x)~6f(x),"t(0,x)=sg(x),xER",(2)v(0,x)~ej(x),yi(0,x)~E900,xER".(3)Herep,q,E>0andf,gii,gEC7(R").Thissystemarisesinphysicsandapplieds.i..ce[1].In1974,H.A.Levine[2]madeuseoftheconcavitymethodshowingthatthesolutionblowsupinfinitetimewithp,q>1andsufficientlylargedata.Veryrecently,K.Deng[31provedthatthereexistsaboundB(n)(5co)suchthatif1相似文献   

带非线性阻尼的粘弹方程解的整体存在性和一致衰减性

研究带有非线性阻尼的粘弹方程,得到了弱解整体存在性和一致指数衰减性.     

反应扩散方程组解的渐近性质

本文利用 L_p 估计、半群理论和 Liapunov 泛函方法,讨论一类反应扩散方程组齐次 Neumann 初边值问题解的渐近性质。证明了解 u(x,t)与其在Ω上的平均(?)(t)有相同的极限。