一类带记忆项的非经典热方程的爆破问题

本文考虑了一类带记忆项的非经典热方程,证明解会在有限时间爆破,而且爆破只会发生在边界.主要结论是:首先利用Green函数与Banach压缩映射定理,建立了问题的经典解;其次,利用经典解,证明了解是有限时间爆破的;最后,证明了一个关于非经典热方程解的性质,利用这个性质,证明了解是在边界上爆破的.     

带奇异项的半线性抛物方程全局解的渐近分析

本文考虑一类带奇异项的半线性抛物方程的初边值问题，利用标准的正则摄动方法和抛物方程的极值原理，对任意给定的正整数Ｎ、得到上述问题的全局古典解的Ｎ＋１阶一致近似计算公式。     

一类带粘性项的抛物方程解的存在性和爆破性

该文研究具有多项式非线性项和粘性项的非线性抛物方程的初边值问题.在一定条件下,我们得到方程的弱解全局存在.在另一些条件下,我们得到该方程的解将在有限时刻爆破,并给出了爆破时间的上界,该上界受初始函数及其支集控制.该结论推广了Messaoudi在文献[15,16]中的工作.     

BLOW-UP AND BLOW-UP RATE FOR A COUPLED SEMILINEAR PARABOLIC SYSTEM WITH NONLOCAL BOUNDARIES

This paper deals with the blow-up properties of positive solutions to a coupled semilinear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. Under appropriate hypotheses, the global existence and finite time blow-up of solutions are proved. Moveover, the upper bound of blow-up rate is obtained.     

THE BLOW-UP PROPERLIES OF SOLUTIONS TO SEMILINEAR HEAT EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

1IntroductionInthispaper,weconsidertheinitial-boundaryvalueproblem,where"o(x)isnon-negativesmoothfunctionsatisfying"o.(0)=0,"o.(1)=1'Whenconsideringtheblow-upofsolution,thefollowingproblemarisenaturally:Doesblow-upoccur?Howdoesthesolutionapproachtheblow-uptime'!Andwilersisthehotspotlocated(blow-upset)?WelookattheheatequationwithanonlillearboundaryconditiollHerefiisaboundeddomaininR",p>1isarealnumber.IthasbeenknownforalongtimethattheDroblelil(1.1).(1.2)withAL(~,0)--'no(x)doesnothaveaglobals…     

BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY

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）.     

SINGULAR SOLUTIONS FOR A CONVECTION DIFFUSION EQUATION WITH ABSORPTION

ＳＩＮＧＵＬＡＲＳＯＬＵＴＩＯＮＳＦＯＲＡＣＯＮＶＥＣＴＩＯＮＤＩＦＦＵＳＩＯＮＥＱＵＡＴＩＯＮＷＩＴＨＡＢＳＯＲＰＴＩＯＮＺｈａｏＪｕｎｎｉｎｇ（赵俊宁）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ１３００２３，Ｃ...     

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS FOR SEMILINEAR HEAT EQUATION ON UNBOUNDED DOMAIN

In this paper, we consider the existence and nonexistence of global solutions to the semilinear heat equation ut - △u = u^p with Neumann boundary value δu/δv= 0 on some unbounded domains, where p > 1, v is the outward normal vector on boundary δΩ. We prove that there exists a critical exponent Pc=Pc(Ω) > 1 such that if p∈(1,pc], for nonnegative and nontrivial initial data, all positive solutions blow up in finite time; if p > Pc, for suitably small nonnegative initial data, there exists a global positive solution.     

BLOW-UP RATE OF SOLUTIONS FOR P-LAPLACIAN EQUATION

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.     

NONTRIVIAL SOLUTIONS FOR A POLYHARMONIC EQUATION WITH SINGULAR TERM

The existence of nontrivial solutions for a polyharmonic equation with singular term is proved by Mountain Pass Lemma and Sobolev-Hardy inequality.     

一类耗散型Camassa-Holm方程的解的爆破

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.     

BIFURCATION RESULTS FOR A SEMILINEAR SCHRODINGER EQUATION WITH INDEFINITE LINEAR PART

This paper studies the following semilinear SchrSdinger problem -Δu v(x)u=λu-g(x)|u|^p-1u,x∈R^N It is proven that there exists a bifurcation branch of solutions for the above problem, when g(x) can possibly vanish except for a bounded domain Ω∈R^N.     

THRESHOLD RESULT FOR SEMILINEAR PARABOLIC EQUATIONS WITH INDEFINITE NON-HOMOGENEOUS TERM

In this paper,we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations ut u=g(u)+λf(x),(x,t)×(0,T),u=0,(x,t)∈×[0,T),u(x,0)=u0(x)≥0,x ∈.(P) By combining a priori estimate of global solution with property of stationary solution set of problem(P),we prove that the minimal stationary solution Uλ(x)of problem(P)is stable,whereas,any other stationary solution is an initial datum threshold for the existence and nonexistence of global solution to problem(P).     

具有非线性边界条件半线性热方程组解的爆破性质

本文考虑一类半线性热方程组的解,给出了解爆破的充分必要条件,爆破速率和爆破点的位置。     

CONVERGENCE OF NUMERICAL SCHEMES FOR A CONSERVATION EQUATION WITH CONVECTION AND DEGENERATE DIFFUSION

The approximation of problems with linear convection and degenerate nonlinear difFusion,which arise in the framework of the transport of energy in porous media with thermodynamic transitions,is done usingθ-scheme based on the centred gradient discretisation method.The convergence of the numerical scheme is proved,although the test functions which can be chosen are restricted by the weak regularity hypotheses on the convection field,owing to the application of a discrete Gronwall lemma and a general result for the time translate in the gradient discretisation setting.Some numerical examples,using both the Control Volume Finite Element method and the Vertex Approximate Gradient scheme,show the role ofθfor stabilising the scheme.     

神经传播型方程解的blow－up

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．     

带有阻尼项的Emden-Fowler方程的区间振动准则

本文研究了带有阻尼项的Emden-Fowler方程.利用广义Riccati变换技巧,给出带有阻尼项的Emden-Fowler方程的振动准则,它推广和改进了文献中的结果,例子说明了结果的应用.     

EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC EQUATION WITH CONVEX AND CONCAVE NONLINEARITIES

In this paper, we consider the existence of positive solutions of the semlinear elliptic boundary value problem with convex and concave nonlinearities, the results obtained improve and generalize some known results.