BLOWUP OF SOLUTIONS TO THE CAUCHY PROBLEM FOR NONLINEARWAVE EQUATIONS

The author proves blow up of solutions to the Cauchy problem of certain nonlinear wave equations and, also, estimates the time when the blow up occurs.     

一般非线性扩散方程Cauchy问题广义解的渐近性质

本文研究了比较一般的非线性扩散方程的Cauchy问题广义解的渐近性质.利用试验函数与积分估计的方法,获得了广义解当t→∞时的渐近性质以及其广义整体解u(x,t),推广了该类方程Cauchy问题广义解的性质.     

关于双曲型方程解的爆破

在RNR+(N2)中考虑非线性双曲型方程 utt-DI(aij(x)Dju)=|u|p-1u.Kato1980年证明了当1<p [SX(]N+1[]N-1[SX)]时,Cauchy问题的解可能在有限时刻爆破.本文使用不同的方法估计, 把Kato的结果改进为1<p<[SX(]N+3[]N-1[SX)].     

一类非线性渗流方程Cauchy问题弱解的存在唯一性

讨论具强非线性源和对流项的一般渗流方程以Ｒ＾Ｎ中某一Ｒａｄｏｎ测度为初始迹的Ｃａｕｃｈｙ问题弱解的存在唯一性。     

Cauchy问题解的不唯一性定理

设P是R~n上常系数m阶齐次线性偏微分算子,m>1,则对于任何给定的正数c、b、ε,下述Cauchy问题 存在非平凡解u,满足     

四阶Ginzburg-Landau型方程的初值问题

本文研究四阶Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ型方程的初值问题,通过建立一般半线性抛物方程的Ｌτ－解和Ｈｓ－解之间的联系,获得该方程的整体Ｈｓ－解的存在唯一性(ｓ＝１、２)。     

GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION

In this paper, the existence and the uniqueness of the local generalized solution and the local classical solution of the Cauchy problem for the generalized BBM-Burgers equationare proved. The existence and the uniqueness of the global generalized solution and the global classical solution for the Cauchy problem of equation （1） are proved when n = 3, 2, 1. Moreover, the decay property of the solution is discussed.     

GLOBALLY SMOOTH SOLUTIONS TO CAUCHY PROBLEM OF A QUASILINEAR HYPERBOLIC SYSTEM ARISING IN BIOLOGY

We consider Cauchy problem of the system of nonlinear conservation lawsut -- (liv). = 0, vf -- uz = 0, (x,t) E R x R , (E)with initial datau(2,0) = u0(2), v(x,0) = v0(x), z E R. (I)It has been 8hown in [1,2],the system (E) describes the maro8copic behaviour of some (so-called"chemOtatic ") bacterial populations, which are attracted by the gradient of some chendcalsubstrate, which they metabolize. When the bacteria have depleted the substrate somewliere,this create8 a gradient in the concen…     

ON THE CLASSIFICATION OF INITIAL DATAFOR NONLINEAR WAVE EQUATIONS

InroductionFor hyperbollc equations the most fundamental problem Is the     

THE CAUCHY PROBLEM FOR A NONLINEAR FAST DIFFUSION EQUATION

In this paper, the existence, uniqueness and continuous dependence on initial data for the Cauchy problem of fast diffusion equation is discussed.     

一类重特征方程柯西问题的存在唯一性

讨论了一类高维重特征方程栖西问题存在唯一性中的离散现象，证明发池方程的参数取某些值时存在唯一性有离散现象发生。并建立了存在唯一性与黎曼问题的联系。     

奇异半线性非局部反应扩散方程Cauchy问题局部解的存在性

本文讨论如下初值问题局部解的存在性 u/ t- (1/ tσ)Δu =(∫RNuλ(t,y) dy) p /λur + f (x) ,t>0 ,x∈ RNlimt→ 0 + u(t,x ) =0 ,　　　　　　　　　　　　　 x∈ RN其中σ>0 ,λ≥ 1,p≥ 0 ,r≥ 1,p+ r>1,f (x)连续有界非负但不恒等于零 ,Δ是 N维 L aplace算子 ,所得结论推广了文献 [2 ,3]的相应结果     

多维拟线性退化抛物方程Cauchy问题解的唯一性和稳定性

本文证明了拟线性退化抛物方程■的Cauchy问题BV解的唯一性和稳定性.     

一种求解修正的Helmholtz方程Cauchy问题的数值方法

本文研究了无界带形区域Ω={(x,y)|0相似文献   

GLOBAL EXISTENCE OF WEAKLY DISCONTIN UOUS SOLUTIONS TO THE CAUCHY PROBLEM WITH A KIND OF NON-SMOOTH INITIAL DATA FOR QUASILINEAR HYPERBOLIC SYSTEMS

The authors consider the Cauchy problem with a kind of non-smooth initial datafor quasilinear hyperbolic systems and obtain a necessary and sufficient condition toguarantee the existence and uniqueness of global weakly discontinuous solution.     

THE EXISTENCE OF GLOBAL SOLUTION AND THE BLOWUP PROBLEM FOR SOME p-LAPLACE HEAT EQUATIONS

This article consider, for the following heat equation ut/|x|s-△pu=uq,(x,t)∈Ω×(0,T), u(x,t)=0,(x,t)∈(?)Ω×(0,T), u(x,0)=u0(x),u0(x)≥0,u0(x)(?)0 the existence of global solution under some conditions and give two sufficient conditions for the blow up of local solution in finite time, whereΩis a smooth bounded domain in RN(N>p),0∈Ω,△pu=div(|▽u|p-2▽u),0≤s≤2,p≥2,p-1相似文献   

A NECESSARY AND SUFFICIENT CONDITION FOR GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO CAUCHY PROBLEM OF QUASILINEAR HYPERBOLIC SYSTEMS IN DIAGONAL FORM

This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form.A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t 0 is obtained,and a sharp estimate of the life span for the classical solution is given.     

高维非线性四阶抛物型方程初值问题全局解

对一类高维非线性四阶抛物型方程初值问题,在初始数据适当小及非线性项适当光滑的情况下,获得了其古典解全局存在性。     

粘性浅水方程柯西问题解的Lp-估计

本文通过对相应线性方程格林函数的估计，而获得粘性浅水方程柯西问题解的Lp渐近估计。