An improved local blow-up condition for Euler-Poisson equations with attractive forcing

We improve the recent result of Chae and Tadmor (2008) [10] proving a one-sided threshold condition which leads to a finite-time breakdown of the Euler-Poisson equations in arbitrary dimension n.     

Boundedness of global positive solutions of a porous medium equation with a moving localized source

In this paper a porous medium equation with a moving localized source ut=ur(Δu+af(u(x₀(t),t))) is considered. It is shown that under certain conditions solutions of the above equation blow up in finite time for large a or large initial data while there exist global positive solutions to the above equation for small a or small initial data. Moreover, in one space dimension case, it is also shown that all global positive solutions of the above equation are uniformly bounded, and this differs from that of a porous medium equation with a local source.     

On the Generalized System of Ferro-magnetic Chain with Gilbert Damping Term

In this paper we have established the existence of global weak solutions and blow-up properties for the generalized system of ferro-magnetic chain with Gilbert damping term by means of Galerkin method and concavity argument. In addltion, the convergence as α → 0 and ε → 0 have also been discussed.     

On Blow-up of Regular Solutions to the Isentropic Euler and Euler-Boltzmann Equations with Vacuum*

In this paper, the authors study the Cauchy problem of n-dimensional isentropic Euler equations and Euler-Boltzmann equations with vacuum in the whole space. They show that if the initial velocity satisfies some condition on the integral J in the “isolated mass group” (see (1.13)), then there will be finite time blow-up of regular solutions to the Euler system with J ≤ 0 (n ≥ 1) and to the Euler-Boltzmann system with J < 0 (n ≥ 1) and J = 0 (n ≥ 2), no matter how small and smooth the initial data are. It is worth mentioning that these blow-up results imply the following: The radiation is not strong enough to prevent the formation of singularities caused by the appearance of vacuum,with the only possible exception in the case J = 0 and n = 1 since the radiation behaves differently on this occasion.     

具有奇性系数的半线性椭圆方程大解的存在性

研究了一类带奇性系数和一般梯度项的半线性椭圆方程大解的存在性. 首先得到解的梯度估计, 然后证明了方程在边界值等于n时解的存在性, 最后利用上下解的方法得到了大解的存在性.     

文“当p→1时,方程-Δu=λup正解的渐近性质”的一点注记

We discuss asymptotic behavior of positive solutions of the equations-Δu=λu^p as p→ 1. Our results improve those in [1].     

一类非线性抛物方程组解的存在性和Blow—up

本文应用上下解方法,给出一类非线性抛物方程组整体解存在的充分必要条件的新结果,并且讨论了其解的Blow-up。     

Blow-up estimates for semilinear parabolic systems coupled in an equation and a boundary condition

This paper deals with the blow-up rate estimates of solutions for semilinear parabolic systems coupled in an equation and a boundary condition. The upper and lower bounds of blow-up rates have been obtained.     

Behaviour of solutions of the quasilinear wave equations for mechanism with a boundary piston possessing mass

1. IntroductionFor the initial-boundary Value problem of the one-dimensional quasilinear wave eqllationwhere ms r, k 2 0 are constants, there are the following known results: For m ~ r = k = 0,[1] obtained the blow-up behaviour for the solution of (1.1), and [2,3] also got the blow-upbehaviour when m = r = 0, k > 0 and m >> 1, r,k > 0 separately. [3-5] discussed thecases of m = k = 0, r > 0 and m ~ 0, r, k > 0 respectively and obtained the existence anduniquness of the global solution.In this …     

Formation of Singularities in One—Dimensional Hydromagnetic Flow

Two results on the formation of singularities in solutions to the system of one-dimensional hydromagnetic dynamics are presented.In particular,it is shown that shocks form from a smooth spatial periodic flow in a finite time if the initial amounts of entropy and the “magnetic field” in each period are smaller than those of sound waves.A quantitative estimate of blow-up time is also given.