一非线性双曲型方程解的爆破

本文应用压缩映射原理证明一非线性双曲型方程的初边值问题存在唯一局部广义解，并给出此问题的广义解爆破的充分条件。     

一类高阶非线性双曲型方程Cauchy问题解的爆破

本文研究一类高阶非线性双曲型方程utt-uxx+μuxxx-αuxxtt+βuxxxxtt=f(ux)x的Cauchy问题,证明问题解的存在性与唯一性,并给出解在有限时刻爆破的充分条件.     

非线性双曲方程解的爆破问题

本文对两类非线性双曲方程的初值问题，研究了因子ｆ（ｔ）对于解爆破的影响。其中一类含ｎ的一次项，对这一类方程的初值问题还研究了ｎ的一次项系数对解爆破的影响．     

一类非线性双曲型方程初边值问题解的爆破

该文给出一类非线性双曲型方程初边值问题解爆破的充分条件, 并证明问题局部解的存在性与唯一性     

一类高阶非线性双曲型方程初边值问题解的爆破

本文研究一类高阶非线性双曲型方程的初边值问题，证明问题局部广义解的存在性与唯一性，同时给出解爆破的充分条件。     

广义神经传播型非线性拟双曲方程解的爆破和熄灭

本文考虑广义神经传播型非线性拟双曲方程具三类边界条件的初边值问题,利用特征函数法,得到了其解在有限时间内爆破和熄灭的条件。     

广州神经传播型非线性拟双曲方程解的爆破和熄灭

本文考虑广义神经传播型非线性拟双曲趴有三类边界条件的初值问题。利用特征函娄和法，得到了其解在有限时间内爆破和熄灭的条件。     

一类广义Boussinesq型方程解的爆破

研究一类广义Boussinesq型方程的初边值问题,利用Galerkin方法证明问题局部广义解的存在性与唯一性．同时,通过使用凸性方法给出问题的解在有限时刻发生爆破的充分条件．     

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.     

BLOWUP OF SOLUTIONS TO THE CAUCHY PROBLEM FOR NONLINEARWAVE EQUATIONS

gi. IntroductionThis paper deals with solutionS of certain nonlinear wave equationS Of the formcorresponding to Antial conditionSwuersis the wave OPerstor.we are interested in showing the ~ up" Of solutions to (1.1)--(1.2). For that, wereIf ac ~ 1)(n ~ 1) > 2, global solutions of ~ equation subject to very general perturbationsof order p exist Provided the initial data are swhciently small (see I6] and references therein).We are also interested in esthaattw the take when "blow up" occurs. …     

ON THE UNIQUENESS OF THE WEAK SOLUTIONS OF A QUASILINEAR HYPERBOLIC SYSTEM WITH A SINGULAR SOURCE TERM

This paper is a continuation of the authors'previous paper[1].In this paper the authorsprove,assuming additional conditions on the initial data,some results about the existence anduniqueness of the entropy weak solutions of the Cauchy problem for the singular hyperbolicsystem a_t+(au)_x_2au/x=0,u_t+1/2(a~2+u~2)_x=0,x>0,t≥0.     

非线性波动方程解的Blow up

本文证明了非线性波动方程的一类小初值问题，当初始能量小于或等于零时，解在有限时间内Ｂｌｏｗｕｐ．并给出当解有有限扩散速度时解的生命区间的上界估计。     

一类非线性反应扩散方程解的Blow—up问题

本文得用极大值原理研究一类非线性反应扩散方程在各种边界条件下解的Ｂｌｏｗ－ｕｐ问题，给出了整体解不存在的一系列定理，并得到了Ｂｌｏｗ－ｕｐ时间Ｔ的上界。     

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS OF THE INITIAL-BOUNDARY VALUE PROBLEM FOR SOME DEGENERATE HYPERBOLIC EQUATION

The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form utt- div(|▽u|p-2▽u)= |u|mu, (x,t) ∈ [0, ∞) ×Ωwith p ＞ 2 and m ＞ 0. He deals with the global solutions by D.H.Sattinger's potential well ideas. At the same time, when the initial energy is positive, but appropriately bounded,the global nonexistence of solutions is verified by using the analysis method.     

OSCILLATION OF NEUTRAL HYPERBOLIC DIFFERNTIAL EQUATION

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｕｒｐｏｓｅｏｆｔｈｉｓｐａｐｅｒｉｓｔｏｅｘｔｅｎｄｓｏｍｅｏｓｃｉｌａｔｉｏｎｒｅｓｕｌｔｓｏｆｔｈｅｐａｐｅｒｓ［１，２］ｔｏｔｈｅｎｅｕｔｒａｌｈｙｐｅｒｂｏｌｉｃｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｏｆｔ...     

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…     

LIFE-SPAN OF CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH SLOW DECAY INITIAL DATA LIFE-SPAN OF CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH SLOW DECAY INITIAL DATA

1. IntroductionConsider the following quasilinear systeman on~ A(u)~ = 0, (1.1)ot oxwhere u ~ (ul,'' t u.)" is the unknown vector function of (t, x) and A(u) ~ (ail(u)) is ann x n matrix with suitably smooth elements ail(u) (i, j = 1,... ) n).Suppose that the system (1.1) is strictly hyperbolic in a neighbourhood of u = 0, namely,for any given u in this domain, A(u) has n distinct real eigenvalues Al(u), AZ(u),'' j A.(u)such thatAl(u) < AZ(u) <'' < A.(u). (1.2)For i = 1,'',nl let h(u…