一类非牛顿渗流方程爆破界的估计

本文利用拟线性常微分方程解的非存在性定理得到了一类拟线性反应扩散方程(非牛顿渗流方程)爆破界的估计,从而推广了半线性反应扩散方程(牛顿渗流方程)相应结果.     

一类非局部反应扩散方程组解的爆破性质

该文研究一类带非局部源项的反应扩散方程组. 作者证明了初值充分大时解在有限时刻爆破, 建立了爆破解的爆破速率估计以及边界层估计.     

一类拟线性抛物型方程组的爆破率和爆破模式

研究了一类非局部退化拟线性抛物型方程组,在齐次Dirichlet边界条件下的正解,在参数和初始数据满足一定的条件下,得到了解的爆破率和爆破模式.     

一类具有粘性项的拟线性抛物型方程组*

研究了一类具有非线性源项和粘性项的拟线性抛物型方程组的初边值问题．通过构造稳定集, 证明了此问题整体解的存在性, 并建立了解的长时间行为．同时在放松函数的适当假设条件下, 得到了初始能量非负时解的爆破性质及解的生命区间估计．     

一类非线性抛物方程组解的爆破时间上下界估计

本文研究了一类非线性抛物方程组uj/t=△uj+fj(u)解的爆破时间的估计问题.通过构造恰当的辅助函数和建立一系列微分不等式,获得了此类非线性抛物方程组解的爆破时间上下界的估计.从而将单个方程的结论推广到了方程组的情形.     

拟线性正对称方程组的边值问题及其对混合型方程的应用

<正> 1.引言 本文有两个目的.第一个目的是讨论拟线性正对称方程组的边值问题.如所知,线性的正对称方程组是一类相当广泛的偏微分方程组,许多常见的偏微分方程都可以化为正对称方程组去.对于这个方程组,可以利用能量不等式来证明许多边值问题的适定性.本文充分利用线性正对称方程组的结果,经过适当的估计,用压缩映照原理证明了拟线性正对称方程组的边值问题的解的存在性.对求解的区域而言,问题是大范围的,但     

一类奇异临界的(p,q)-Laplacian拟线性方程组非负基态解的存在性

研究了一类含Sobolev临界指数的奇异(p,q)-Laplacian拟线性椭圆方程组,利用变分方法,结合Nehari流形和集中紧性原理证明对应的能量泛函满足局部(PS)条件,得到了这类方程组非负基态解的存在性.     

一类临界拟线性椭圆型方程组解的存在性

本文讨论了一类临界拟线性椭圆型方程组解的存在性问题.利用LionsPL提出的第二集中紧性原理和山路引理,证明了该方程组在超线性扰动情形下非平凡解的存在性.此外,利用极值原理,也得到了该方程组在次线性扰动情形存在非平凡解.     

一类半线性抛物型方程组解的爆破速率估计

考虑一类带有齐次Dirichlet边界条件且反应项分别为指数形式和幂函数形式的半线性抛物型方程组,利用比较原理得到了方程解爆破的充分条件,由数学分析原理和最大值原理得到了爆破解的爆破速率估计.     

具有多重非局部源的反应扩散方程组解的爆破性质（英文）

在本文中,我们研究一类具有多重非局部源的反应扩散方程组的齐次第一初边值问题.通过应用比较原理和伸缩变换的方法,得到解的两个分量发生同时或非同时爆破的最优判据.在此基础上,进一步得到所有可能情形的爆破速率.该结果推广了文[8]中的相关结果.     

Nonexistence of positive solutions to a quasilinear elliptic system and blow-up estimates for a non-Newtonian filtration system

The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic differential equations first. Then the result of nonexistence for a differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blow-up estimates for a class of quasilinear reaction-diffusion systems (non-Newtonian filtration systems) are established to extend the result of semilinear reaction-diffusion (Fujita type) systems.     

Blow-up estimates of positive radial solutions of a class first-order evolution systems

We derive the nonexistence of radially positive solutions for a system of quasilinear elliptic differential equations, and establish blow-up estimates for a class of first-order evolution systems (in time). The main results are new and extend previous known results.     

Non-existence of positive solution to a quasilinear elliptic system and blow-up estimates for a reaction-diffusion system

IntroductionIn these years, the reaction-diffusion systems of Fujita typea5 ttell as the related elliptic systemt'ith fl g RN, Tnl. n1 3 0, i = 1, 2. \vere studied by' a nu111ber of authors. The probiemsconcerning system (l) inc1ude globa1 existence and g1obal existen(.e numbers. b1ow-up. bloxv-uprates, and blow-up sets. uniqueness or nonuniqueness. et('. FOr s}'stem (2) there are problemssuch as existence or non-existence. uniqueness or nonllniqueI1ess. and so ol1. 1Ieanwhile. itseems that…     

Nonlinear oscillations of fourth order quasilinear ordinary differential equations

We consider fourth order quasilinear ordinary differential equations. Firstly, we classify positive solutions into four types according to their asymptotic properties. Then we derive existence theorems of positive solutions belonging to each type. Using these results, we can obtain an oscillation criterion, which is our main objective. Moreover, applying such criteria for ordinary differential equations to binary elliptic systems, we establish nonexistence theorems for positive solutions.     

Non-existence of positive radial solutions for a class of quasilinear elliptic system

In this paper, our main purpose is to establish some nonexistence results of positive radial solutions to the quasilinear ordinary differential equation system. The main results of the present paper are new and extend the previously known results.     

Existence and nonexistence results for reaction-diffusion equations in product of cones

Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.     

On differential inequalities with point singularities on the boundary

We prove the nonexistence of solutions for some nonlinear ordinary differential equations and inequalities, for quasilinear partial differential equations and inequalities in bounded domains with singular points on the boundary, and for systems of such equations and inequalities. The proofs are based on the method of nonlinear capacity. We also give examples demonstrating that the conditions obtained are sharp in the class of problems under consideration.     

Some Notes on Reaction Diffusion Systems with Nonlinear Boundary Conditions

This paper deals with the existence and nonexistence of global positive solution to a semilinear reaction-diffusion system with nonlinear boundary conditions.For the heat diffusion case,the necessary and sufficient conditions on the global existence of all positive solutions are obtained.For the general fast diffusion case,we get some conditions on the global existence and nonexistence of positive solutions.The results of this paper fill the some gaps which were left in this field.     

Blow-up for a degenerate parabolic equation with nonlocal source and nonlocal boundary

In this article, we investigate the blow-up properties of the positive solutions for a doubly degenerate parabolic equation with nonlocal source and nonlocal boundary condition. The conditions on the existence and nonexistence of global positive solutions are given. Moreover, we give the precise blow-up rate estimate and the uniform blow-up estimate for the blow-up solution.     

Properties of positive solutions to a nonlinear parabolic problem

This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vazquez and the comparison principle, we deduce that the blow-up occurs only on the boundary (?)Ω. In addition, for a bounded Lipschitz domainΩ, we establish the blow-up rate estimates for the positive solution to this problem with a= 0.