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1.
一类非局部反应扩散方程组Cauchy问题的临界爆破指标   总被引:4,自引:0,他引:4  
张丽琴 《数学研究》2001,34(2):136-141
证明了一类来源于燃烧理论的非局部反应扩散方程组Cauchy问题解的局部存在性、唯一性及临界爆破指标的存在性。并证明临界爆破指标属于爆破情形。  相似文献   

2.
本文讨论了一类反应扩散方程组齐次第一初边值问题u_t=△u+u~mv~p,v_t=△v+u~qv~n的不同时爆破临界指标问题.在一定初值条件下,本文给出了径向解的四种同时、不同时爆破现象:存在初值使得同时爆破或不同时爆破发生;任何爆破均是同时或不同时的.通过对指标参数的完整分类给出了四种爆破现象的充分必要条件,并且得到了解的全部爆破速率估计.所得结果推广了以前的相应工作.  相似文献   

3.
一类半线性抛物方程组的爆破临界指标   总被引:3,自引:0,他引:3  
本文考察一类半线性抛物方程组的Cauchy问题,计算出了该问题的爆破临界指标。  相似文献   

4.
本文研究了具有非局部边界条件和非线性内部源的多孔介质抛物型方程组问题。利用比较原理,获得了权函数和系数对整体解和爆破解的影响,并得到了解的爆破临界指标,推广了先前的研究结果。  相似文献   

5.
带调和势的非线性Schrdinger方程爆破解的L~2集中率   总被引:1,自引:0,他引:1  
李晓光  张健 《数学学报》2006,49(4):909-914
本文讨论了带调和势的具有临界幂的非线性Schrodinger方程,得到其爆破解在t→T(爆破时间)的L2集中率.  相似文献   

6.
本文讨论具齐次Dirichlet边界条件非局部源反应扩散方程组的爆破解,给出四类同时爆破与不同时爆破现象的判定指标,这四类爆破现象包含:(i)存在不同时爆破;(ii)同时爆破与不同时爆破共存;(iii)任意爆破必是同时爆破;(iv)任意爆破必是不同时爆破.  相似文献   

7.
本文讨论了带调和势的具有临界幂的非线性Schrodinger方程,得到其爆破解在t→T(爆破时间)的L2集中率.  相似文献   

8.
主要研究了具有混合型的多重非线性项的抛物方程组的初边值问题.方程组中的非线性项是幂函数和指数混合型的.这些非线性项组合出了源-流交叉耦合,通过比较原理得到了方程组的上下解,并得到了解有限时刻爆破的临界指标.  相似文献   

9.
研究了在光滑有界域中带有变指数的拟线性椭圆方程组,且该方程组满足边界爆破的条件,在常指数的基础上进一步深入讨论了变指数的情况.主要运用了构造上下解和迭代的方法证明了边界爆破解在临界与次临界条件下,解的存在性,唯一性以及边界行为.  相似文献   

10.
研究非线性Klein-Gordon方程的初边值问题,运用位势井方法,在E(0)d的情况得到了方程解的整体存在和爆破.在临界能量状态得到了整体解的存在性与不存在性.最后使用凸性方法,得到某些具有高初始能量解的爆破.  相似文献   

11.
We study an elliptic problem involving critical Sobolev exponent in domains with small holes. We prove the existence of solutions which blow up like a volcano near the centre of each hole.  相似文献   

12.
In this paper, we prove sharp blow up and global existence results for a heat equation with nonlinear memory. It turns out that the Fujita critical exponent is not the one which would be predicted from the scaling properties of the equation.  相似文献   

13.
We study the asymptotic behavior of positive solutions of fully nonlinear elliptic equations in a ball, as the exponent of the power nonlinearity approaches a critical value. We show that solutions concentrate and blow up at the center of the ball, while a suitable associated energy remains invariant.  相似文献   

14.
In this paper we make the analysis of the blow up of low energy sign-changing solutions of a semilinear elliptic problem involving nearly critical exponent. Our results allow to classify these solutions according to the concentration speeds of the positive and negative part and, in high dimensions, lead to complete classification of them. Additional qualitative results, such as symmetry or location of the concentration points are obtained when the domain is a ball.  相似文献   

15.
This paper deals with asymptotic behavior for blow‐up solutions to time‐weighted reaction–diffusion equations utu+eαtvp and vtv+eβtuq, subject to homogeneous Dirichlet boundary. The time‐weighted blow‐up rates are defined and obtained by ways of the scaling or auxiliary‐function methods for all α, . Aiding by key inequalities between components of solutions, we give lower pointwise blow‐up profiles for single‐point blow‐up solutions. We also study the solutions of the system with variable exponents instead of constant ones, where blow‐up rates and new blow‐up versus global existence criteria are obtained. Time‐weighted functions influence critical Fujita exponent, critical Fujita coefficient and formulae of blow‐up rates, but they do not limit the order of time‐weighted blow‐up rates and pointwise profile near blow‐up time. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

16.
We study the global and blow-up solutions for a strong degenerate reaction–diffusion system modeling the interactions of two biological species. The local existence and uniqueness of a classical solution are established. We further give the critical exponent for reaction and absorption terms for the existence of global and blow-up solutions. We show that the solution may blow up if the intraspecific competition is weak. This supports ecologist A.J. Nicholson’s conclusion that intraspecific competition is the main factor regulating population size.  相似文献   

17.
It is well known that the heat kernel in the hyperbolic space has a different behavior for large times than the one in the Euclidean space. The main purpose of this paper is to study its effect on the positive solutions of Cauchy problems with power nonlinearities. Existence and non-existence results for local solutions are derived. Emphasis is put on their long time behavior and on Fujita?s phenomenon. To have the same situation as for the Cauchy problem in RN, namely finite time blow up for all solutions if the exponent is smaller than a critical value and existence of global solutions only for powers above the critical exponent, we must introduce a weight depending exponentially on the time. In this respect the situation is similar to problems in bounded domains with Dirichlet boundary conditions. Important tools are estimates for the heat kernel in the hyperbolic space and comparison principles.  相似文献   

18.
This letter is concerned with the blow-up of the solutions to a semilinear parabolic problem with a reaction given by a variable exponent. Lower bounds for the time of blow-up are derived if the solutions blow up.  相似文献   

19.
This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that pc = (σ+m)n/(n-σ-2) is its critical exponent provided max{-1, [(1-m)n-2]/(n+1)} σ n-2. This critical exponent is not the same as that for the corresponding equations with the boundary value 0, but is more closely tied to the critical exponent of the elliptic type degenerate equations. Furthermore, we demonstrate that if max{1, σ + m} p ≤ pc, then every positive solution of the equations blows up in finite time; whereas for ppc, the equations admit global positive solutions for some boundary values and initial data. Meantime, we also demonstrate that its positive solutions blow up in finite time provided n ≤σ+2.  相似文献   

20.
This paper concerns the asymptotic behavior of solutions to one-dimensional semilinear parabolic equations with boundary degeneracy both in bounded and unbounded intervals. For the problem in a bounded interval, it is shown that there exist both nontrivial global solutions for small initial data and blowing-up solutions for large one if the degeneracy is not strong. Whereas in the case that the degeneracy is strong enough, the nontrivial solution must blow up in a finite time. For the problem in an unbounded interval, blowing-up theorems of Fujita type are established. It is shown that the critical Fujita exponent depends on the degeneracy of the equation and the asymptotic behavior of the diffusion coefficient at infinity, and it may be equal to one or infinity. Furthermore, the critical case is proved to belong to the blowing-up case.  相似文献   

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