共查询到20条相似文献,搜索用时 78 毫秒
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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
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Li Fucai 《偏微分方程(英文版)》2005,18(4):327-340
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《数学物理学报(B辑英文版)》2020,(4)
In this article, we study the blow-up solutions for a case of b-family equations.Using the qualitative theory of differential equations and the bifurcation method of dynamical systems, we obtain five types of blow-up solutions: the hyperbolic blow-up solution, the fractional blow-up solution, the trigonometric blow-up solution, the first elliptic blow-up solution, and the second elliptic blow-up solution. Not only are the expressions of these blow-up solutions given, but also their relationships are discovered. In particular, it is found that two bounded solitary solutions are bifurcated from an elliptic blow-up solution. 相似文献
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Cao Zhenchao 《数学研究》1994,27(1):45-50
BLOW-UPATTHEBOUNDARYFORDEGENERATEDIFFUSIONEQUATION¥CaoZhenchao(Dept.ofMath.,XiamenUniv.Xiamen361005)Abstract:Inthispaperconsi... 相似文献
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In this article, we study the blow-up phenomena of generalized double dispersion equations u_(tt)-u_(xx)-u_(xxt) + u_(xxxx)-u_(xxtt)= f(u_x)_x.Under suitable conditions on the initial data, we first establish a blow-up result for the solutions with arbitrary high initial energy, and give some upper bounds for blow-up time T~* depending on sign and size of initial energy E(0). Furthermore, a lower bound for blow-up time T~* is determined by means of a differential inequality argument when blow-up occurs. 相似文献
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In this article,we study the initial boundary value problem of generalized Pochhammer-Chree equation u_(tt)-u_(xx)-u_(xxt)-u_(xxtt)=f(u) xx,x ∈Ω,t 0,u(x,0) = u0(x),u t(x,0)=u1(x),x ∈Ω,u(0,t) = u(1,t) = 0,t≥0,where Ω=(0,1).First,we obtain the existence of local W k,p solutions.Then,we prove that,if f(s) ∈ΩC k+1(R) is nondecreasing,f(0) = 0 and |f(u)|≤C1|u| u 0 f(s)ds+C2,u 0(x),u 1(x) ∈ΩW k,p(Ω) ∩ W 1,p 0(Ω),k ≥ 1,1 p ≤∞,then for any T 0 the problem admits a unique solution u(x,t) ∈ W 2,∞(0,T;W k,p(Ω) ∩ W 1,p 0(Ω)).Finally,the finite time blow-up of solutions and global W k,p solution of generalized IMBq equations are discussed. 相似文献
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神经传播型方程解的blow-up 总被引:4,自引:0,他引:4
本文研究神经传播型非线性拟双曲方程Utt-△ut=f(u)ut+g(u)O)的初边值问题与初值问题解的blow-up问题,不但研究了对任意非负初值解的blow-up,而且利用一种改进了的特征函数法研究了对充分大初值解的blow-up. 相似文献
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本文研究了带耗散项λuxx的Camassa-Holm方程的局部适定性和爆破现象.由Kato定理得到局部适定性的结果,证明了解的爆破机制,并且证明了当初值满足一定条件时解发生爆破,最后研究了爆破解的爆破率. 相似文献
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退化的抛物方程组解的全局存在及爆破 总被引:2,自引:2,他引:0
本文讨论了退化抛物方程组初边值问题解的性质 ,通过构造上、下解 ,证明了古典解的存在唯一性 ,利用特征函数以及最大值原理 ,得出了解全局存在以及爆破的若干条件 . 相似文献
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This paper investigates the finite time blow-up of nonnegative solutions for a nonlinear diffusion system with a more complicated source term,which is a product of localized source,local source,and weight function,and complemented by homogeneous Dirichlet boundary conditions.The criteria are proposed to identify simultaneous and nonsimultaneous blow-up solutions.Moreover,the related classification for the four parameters in the model is optimal and complete.The results extend those in Zhang and Yang [12]. 相似文献
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《数学物理学报(B辑英文版)》2020,(3)
In this article, we focus on the short time strong solution to a compressible quantum hydrodynamic model. We establish a blow-up criterion about the solutions of the compressible quantum hydrodynamic model in terms of the gradient of the velocity, the second spacial derivative of the square root of the density, and the first order time derivative and first order spacial derivative of the square root of the density. 相似文献
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吴艺婷 《数学物理学报(B辑英文版)》2024,(2):609-631
In this paper,we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs.Under some appropriate assumptions on the curvature condition CDE’(n,0),the polynomial volume growth of degree m,the initial values,and the exponents in absorption terms,we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time.Our current work extends the results achieved by Lin and Wu(Calc Var Partial Differ Equ,2017,56:Art 102) and Wu(Rev R ... 相似文献
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《数学物理学报(B辑英文版)》2016,(1)
In this paper, we consider the formation of singularity for the classical solutions to compressible MHD equations without thermal conductivity or infinity electric conductivity when the initial data contains vacuum. We show that the life span of any smooth solution will not be extended to ∞, if the initial vacuum only appears in some local domain and the magnetic field vanishes on the interface that separates the vacuum and non-vacuum state,regardless the size of the initial data or the far field state. 相似文献
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《数学物理学报(B辑英文版)》2017,(6)
In this paper,we consider the short time classical solution to a simplified hydrodynamic flow modeling incompressible,nematic liquid crystal materials in R~3. We establish a criterion for possible breakdown of such solutions at a finite time. More precisely,if(u,d)is smooth up to time T provided that ∫_0~T||▽×u(t,·)||_(BMO)(R~3)+||▽d(t,·)||_(L~4(R~3))~8dt∞. 相似文献
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本文利用Fourier空间的比较原理研究一类拟线性拟抛物方程解的Blow-up问题,并给出了其解在有限时刻Blow-up的条件。 相似文献
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本文给出了理想磁流体动力学方程组的经典解在初始扰动适当大的情况下破裂的结果.文[1]证明了描述多方理想可压缩气体运动的欧拉系统的经典解在初始扰动适当大的情况下破裂的结果.本文将利用和文[1]相似的方法证明所得定理. 相似文献
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