Blow-up of the Solutions of the Initial Boundary Value Problem of Camassa-Holm Equation

Any classical non-null solution to the initial boundary value problem of Camassa-Holm equation on finite interval with homogeneous boundary condition must blow up in finite time. An initial boundary value problem of CamassaHolm equation on half axis is also investigated in this paper. When the initial potential is nonnegative,then the classical solution exists globally; if the derivative of initial data on zero point is nonpositire, then the life span of nonzero solution nmst be finite.

Blow-Up of Solution to Cauchy Problem for the Singularly Perturbed Sixth-Order Boussinesq-Type Equation

We consider the singularly perturbed sixth-order Boussinesq-type equation, which describes the bidirectional propagation of small amplitude and long capillary gravity waves on the surface of shallow water for bond number (surface tension parameter) less than but very close to 1/3. The sufficient conditions of blow-up of solution to the Cauchy problem for this equation are given.

奇异半线性抛物方程初值问题解的存在性与不存在性,Blow-up问题及解的无限增长性

该文研究一类奇异半线性抛物方程初值问题的非负局部解存在与不存在的条件，解的BloW-Up问题及当t时解的无限增长性．

奇异半线性发展方程组解的Blow-up问题

讨论奇异半线性发展方程组解的B low-up问题时,通常先对解进行估计,然后讨论在一定条件下解的B low-up.论文继续用这种方法讨论奇异半线性发展方程组解的B low-up问题,得到一定条件下解会B low-up.

一类变系数半线性热方程初值问题解的 blow-up 问题

本文讨论下面的初值问题ｕｔ－１ｔΔｕ＝ｕγｕ（ε０，ｘ）＝φ（ｘ）｛ｔ＞ε０＞０ｘ∈Ｒｎ（０．１）ｘ∈Ｒｎ．（０．２）其中γ１，φ（ｘ）连续有界，且φ（ｘ）０但不恒为零。我们证明了当１γ－１ｎ２时，初值问题（０．１）（０．２）的非负解必在有限时间ｂｌｏｗ－ｕｐ。即问题（０．１）（０．２）在１γ－１ｎ２时没有非负的整体解。

人口问题中具广义Ginzbur-Landau型方程解的渐近性和Blow-up

在文献[1][2][3]和[4]的基础上,研究人口问题中具广义Ginzbur-Landau 型弥散方程(0.21),(0.22)及更一般的非线性高阶抛物型方程(0.23)初边值问题,在古典解存在且唯一的条件下,利用文[7,8]的相应方法,深入探讨问题的广义解和古典解的渐近性及Blow-up 现象,得到许多新结果.

非线性Sobolev-Galpern方程解的blow up

本文研究非线性 Sobolev-Galpern方程的初边值问题整体解的不存在性即解的爆破问题 .用能量估计方法并借助于 Jensen不等式证明了非线性

非线性反应扩散方程解的Blow-up问题

研究了非线性反应扩散方程ut=Δu+f(u)初边值问题的解的Blow up问题,证明了其光滑解只能在一个有界区间内存在。利用引入的"高斯函数"得到了一些新的非整体存在的充分条件,这些条件对Lp解也普遍适用。此外,对有关结果进行了相应的简化与改进。

非线性反应扩散方程解的Blow-up问题

考虑反应扩散方程初边值问题ｕｔ＝Ｌｕ＋ｆ（ｕ），Ω×（ｏ，Ｔ）βｕν＋ｕΩ＝ｈ（ｕ），（Ｅ）ｕ（ｘ，０）＝ｕ０（ｘ）解的Ｂｌｏｗ－ｕｐ问题，其中：Ｌ≡∑ｎｉ，ｊ＝１ｘｉｉｊｘｊ＋∑ｎｉ＝１ｉｘｉ是椭圆算子，β是常数，０＜β＜＋∞，Ω是Ｒｎ中的有界区域，ｕν是关于（ａｉｊ）在Ω上的余法向导数。在ｆ和ｇ的适当条件下，证明了问题（Ｅ）的光滑解只能在一个有界区间〔０，Ｔ０）存在，即有：ｌｉｍｔ→Ｔ－０ｓｕｐｘ∈Ωｕ（ｘ，ｔ）＝＋∞推广了前人的工作。

具耗散与磁场效应的非线性Schrdinger型方程组解的Blow-up

本文考虑具耗散与磁场效应的非线性Schrodinger型方程组的初边值问题在对u_0(x),q(s),γ(t),Ω和n加适当条件下.得到该问题解的blow-up.

半线性拟抛物方程古典解的Blow-up问题

研究了半线性拟抛物方程的初边值问题ut-Δut=f(u)x∈Ω,t>0(1.1)u(x,0)=u0(x),x∈Ω(1.2)u|Ω=0,t≥0(1.3)古典解的blow-up性.讨论了正解的存在性.研究了(1.1)^(1.3)的古典解u(x,t)的blow-up性,即存在T0≤(1+λ0)∫α∞g-1(x)ds使得limt→T0-‖u‖p=∞对1≤p≤∞.

一类拟线性抛物方程解的blow-up

在文 [4 ]的基础上 ,用能量估计法研究了非线性抛物方程ut- ∑nt,j=1 xi(aij(x) u xj) - Δut=f(x,t,u,Du)初边值问题解的 blow- up性质 ,得到了解发生 blow- up的条件 .

一相非平衡问题Blow-up的一点注记

构造一个一相非平衡问题Ｂｌｏｗ－ｕｐ的例子，说明这类问题的整体解不一定存在．

一类奇异半线性发展方程组解的Blow-up问题

讨论了一类具有奇异系数的发展方程组Cauchy问题的解在有限时间内的blow-up问题,并给出了相应的一些结果.

一类奇异半线性反应扩散方程组Cauchy问题解的Blow-up问题

研究了如下奇异半线性反应扩散方程组Cauchy问题:ut-(1/t)Δu=vp t>ε>0,x∈Rnvt-(1/t)Δv=up t>ε>0,x∈Rn(1)limt→εu(t,x)=u0(x)x∈Rnlimt→εv(t,x)=v0(x)x∈Rn(2)其中,p>1,u0(x),v0(x)∈L∞(Rn),u0(x)≥0,v0(x)≥0,且u0(x),v0(x)不恒为零.证明了其非负局部解在有限时间内Blow-up.

具耗散与磁场效应的非线性Schrodinger型方程组解的Blow-up

本文考虑具耗散与磁场效应的非线性Schrodinger型方程组 i■=△■+q(|■|~2)■+η■x(■x■)-i/2(t)■。的初边值问题,在适当的条件下得到了解的blow-up性质。

EXISTENCE TIME OF SOLUTION OF THE (1+2)D KNOBLOCH EQUATION WITH INITIAL-BOUNDARY VALUE PROBLEM

The equation of pattern formation induced by buoyancy or by surface-tension gradient in finite systems confined between horizontal poor heat conductors is introduced by Knobloch[1990] where u is the planform function, μ is the scaled Rayleigh number, K = 1 and α represents the effects of a heat transfer finite Blot number. The cofficients β, δ and γ do not vanish when the boundary, conditions at top and bottom are not identical (β / 0, δ / 0) or nonBoussinesq effects are taked into account (γ / 0). In this paper, the Knobloch equation with α > 0 is considered, the global existence in L2-space and the finite existence time of solution in V2-space have been obtained respectively.

Initial value problem for a class of fourth-order nonlinear wave equations

In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.

Blow-up of solution for a generalized Boussinesq equation

This paper studies the initial boundary value problem for a generalized Boussinese equation and proves the existence and uniqueness of the local generalized solution of the problem by using the Galerkin method. Moreover, it gives the sufficient conditions of blow-up of the solution in finite time by using the concavity method.

GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO A NONLOCAL EVOLUTION p-LAPLACE SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS

In this paper, the authors discuss the global existence and blow-up of the solution to an evolution p-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local existence of solutions, then give a necessary and sufficient condition on the global existence of the positive solution.