共查询到20条相似文献,搜索用时 78 毫秒
1.
In this paper we work with the ordinary diffential equation u′′ u3 = 0 and obtain some interesting phenomena concerning blow-up, blow-up rate, life-spann, zeros and critical points of solutions to this equation. 相似文献
2.
《数学物理学报(B辑英文版)》2015,(5)
In this paper, we work with the ordinary differential equationn2u(n)′′=u(n)p and obtain some interesting phenomena concerning, boundedness, blow-up, blow-up rate,life-span of solutions to those equations. 相似文献
3.
李明融 《数学物理学报(B辑英文版)》2007,(4)
In this article the author works with the ordinary differential equation u″= |u|~p for some p>0 and obtains some interesting phenomena concerning blow-up,blow-up rate,life-span,stability,instability,zeros and critical points of solutions to this equation. 相似文献
4.
Yue-Loong CHANG Meng-Rong LI C.Jack YUE Yong-Shiuan LEE Tsung-Jui CHIANG-LIN 《数学物理学报(B辑英文版)》2018,(4)
In this article, we work with the ordinary equation u〞-n~(-q-1)u(n)~q= 0 and learn some interesting phenomena concerning the blow-up and the blow-up rate of solution to the equation. 相似文献
5.
李明融 《数学物理学报(B辑英文版)》2007,27(4):703-734
In this article the author works with the ordinary differential equation u" = |u|^p for some p 〉 0 and obtains some interesting phenomena concerning blow-up, blow-up rate, life-span, stability, instability, zeros and critical points of solutions to this equation. 相似文献
6.
Zhao Junning Liang Zhilei 《偏微分方程(英文版)》2008,21(2):134-140
In this note we consider the blow-up rate of solutions for p-Laplacian equation with nonlinear source, ut = div(|↓△u|p-2↓△u)+uq, (x, t) ∈ RN × (0, T), N ≥ 1. When q 〉 p - 1, the blow-up rate of solutions is studied. 相似文献
7.
李明融 《数学物理学报(B辑英文版)》2010,(4):1227-1234
In this article, we study the following initial value problem for the nonlinear equation
{u″u(t)=c1+c2u′(t)^2, c1≥0, c2≥0,
u(0)=u0, u′(0)=u1.
We are interested in properties of solutions of the above problem. We find the life-span, blow-up rate, blow-up constant and the regularity, null point, critical point, and asymptotic behavior at infinity of the solutions. 相似文献
{u″u(t)=c1+c2u′(t)^2, c1≥0, c2≥0,
u(0)=u0, u′(0)=u1.
We are interested in properties of solutions of the above problem. We find the life-span, blow-up rate, blow-up constant and the regularity, null point, critical point, and asymptotic behavior at infinity of the solutions. 相似文献
8.
原保全 《数学物理学报(B辑英文版)》2010,(5):1469-1480
In this article,we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid equations in R~3.We obtain the classical blow-up criteria for smooth solutions(u,ω,b),i.e.,u ∈ L q(0,T;L p(R 3)) for 2 q + 3 p ≤ 1 with 3p≤∞,u ∈ C([0,T);L 3(R 3)) or u ∈L q(0,T;L p) for 3 2p≤∞ satisfying 2 q + 3p≤2.Moreover,our results indicate that the regularity of weak solutions is dominated by the velocity u of the fluid.In the end-point case p = ∞,the blow-up criteria can be extended to more general spaces u∈ L~1(0,T;B_(∞,∞)~0(R~3)). 相似文献
9.
This paper deals with the blow-up of positive solutions of the uniformly pa-rabolic equations ut = Lu + a(x)f(u) subject to nonlinear Neumann boundary conditions . Under suitable assumptions on nonlinear functi-ons f, g and initial data U0(x), the blow-up of the solutions in a finite time is proved by the maximum principles. Moreover, the bounds of "blow-up time" and blow-up rate are obtained. 相似文献
10.
This paper deals with the blow-up properties of solutions to a system of semilinear heat equations with the boundary conditions u(x,t)=v(x,t)=0 on SR×[0,T).The exact estimates on blow-up rate of solutions are established. 相似文献
11.
Zhi Wen DUAN Kwang Ik KIM 《数学学报(英文版)》2007,23(6):1083-1094
This paper is concerned with a nonlocal hyperbolic system as follows utt = △u + (∫Ωvdx )^p for x∈R^N,t〉0 ,utt = △u + (∫Ωvdx )^q for x∈R^N,t〉0 ,u(x,0)=u0(x),ut(x,0)=u01(x) for x∈R^N,u(x,0)=u0(x),ut(x,0)=u01(x) for x∈R^N, where 1≤ N ≤3, p ≥1, q ≥ 1 and pq 〉 1. Here the initial values are compactly supported and Ω belong to R^N is a bounded open region. The blow-up curve, blow-up rate and profile of the solution are discussed. 相似文献
12.
In this paper, we give some results on the blow-up behaviors of the solution to the mixed problem for some higher nonlinear hyperbolic evolution equation in finite time. By introducing the "blow-up factor K(u,ut)" we get some new results, which generalize the conclusions of [3] and [4]. 相似文献
13.
《数学学报》2016,(4)
正Long Time Dynamics of the 3D Radial NLS with the Combined Terms Gui Xiang XU Jian Wei Yang Abstract In this paper,we study the scattering and blow-up dichotomy result of the radial solution to nonlinear Schr(o|¨)dinger equation(NLS)with the combined terms iu_t+△u=-|u|~4u+|u|~(p-1)u,1+4/3p5in energy space H~1(R~3).The threshold energy is the energy of the ground state W of the focusing,energy critical NLS,which means that the subcritical perturbation does not affect the determination of threshold,but affects the scattering and blow-up dichotomy result with 相似文献
14.
In this paper,we deal with the blow-up property of the solution to the diffusion equation u_t = △u + a(x)f(u) ∫_Ωh(u)dx,x∈Ω,t0 subject to the null Dirichlet boundary condition.We will show that under certain conditions,the solution blows up in finite time and prove that the set of all blow-up points is the whole region.Especially,in case of f(s) = s~p,h(s) = s~q,0 ≤ p≤1,p + q 1,we obtain the asymptotic behavior of the blow up solution. 相似文献
15.
GALAKTIONV V.A. 《偏微分方程(英文版)》2010,(2):105-146
Blow-up behaviour for the fourth-order quasilinear porous medium equation with source,ut=-(|u|^nu)xxxx+|u|^p-1u in R×R+,where n 〉 0, p 〉 1, is studied. Countable and finite families of similarity blow-up patterns of the form us(x,t)=(T-t)^-1/p-1f(y),where y=x/(T-t)^β' β=p-(n+1)/4(p-1),which blow-up as t → T^- 〈∞ are described. These solutions explain key features of regional (for p = n+1), single point (for p 〉 n+1), and global (for p ∈ (1,n+1))blowup. The concepts and various variational, bifurcation, and numerical approaches for revealing the structure and multiplicities of such blow-up patterns are presented. 相似文献
16.
This paper deals with a class of porous medium equation ut=△u^m+f(u)with homogeneous Dirichlet boundary conditions. The blow-up criteria is established by using the method of energy under the suitable condition on the function f(u). 相似文献
17.
In this paper,we study the scattering and blow-up dichotomy result of the radial solution to nonlinear Schrodinger equation(NLS) with the combined terms iu_t+△u=-|u|~4u+|4|~(p-1)u,1+4/3p5 in energy space H~1(R~3).The threshold energy is the energy of the ground state W of the focusing,energy critical NLS,which means that the subcritical perturbation does not affect the determination of threshold,but affects the scattering and blow-up dichotomy result with subcritical threshold energy.This extends algebraic perturbation in a previous work of Miao,Xu and Zhao[Comm.Math.Phys.,318,767-808(2013)]to all mass supercritical,energy subcritical perturbation. 相似文献
18.
For 2 γ min{4, n}, we consider the focusing Hartree equation iu_t+ △u +(|x|~(-γ)* |u|~2)u = 0, x ∈ R~n.(0.1)Let M [u] and E [u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of-△ Q + Q =(|x|~(-γ)* |Q|~2)Q. Guo and Wang [Z. Angew. Math.Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of(0.1) if M [u]~(1-s_c)E [u]~(s_c) M [Q]~(1-s_c)E [Q]~(s_c)(s_c=(γ-2)/2). In this paper, we consider the complementary case M [u]~(1-s_c)E [u]~(s_c)≥ M [Q]~(1-s_c)E [Q]~(s_c) and obtain a criteria on blow-up and global existence for the Hartree equation(0.1). 相似文献
19.
《数学学报(英文版)》2021,(9)
We study the Cauchy problem for the Davey–Stewartson equation i?_tu + Δu + |u|~2 u + E_1(|u|~2)u = 0,(t, x) ∈ R × R~3.The dichotomy between scattering and finite time blow-up shall be proved for initial data with finite variance and with mass-energy M(u_0)E(u_0) above the ground state threshold M(Q)E(Q). 相似文献
20.
Chen Youpeng 《高校应用数学学报(英文版)》2007,22(2):213-225
In this paper there are established the global existence and finite time blow-up results of nonnegative solution for the following parabolic systemut=Δu vp(x0, t)-aur, x∈Ω, t>0,vt=Δv uq(x0,t)-bvs, x∈Ω, t>0subject to homogeneous Dirichlet conditions and nonnegative initial data, where x0 ∈Ω is a fixed point, p, q, r, s ≥ 1 and a, b > 0 are constants. In the situation when nonnegative solution (u, v) of the above problem blows up in finite time, it is showed that the blow-up is global and this differs from the local sources case. Moreover, for the special case r = s = 1,are obtained uniformly on compact subsets of Ω, where T* is the blow-up time. 相似文献