一类四阶非线性波动方程的初边值问题

本文研究一类描述非线性粘弹性杆中纵波振动的非线性波动方程的初边值问题,用Ｇａｌｅｒｋｉｎ方法证明了其整体强解的存在性,唯一性,最后讨论了解的渐近性质及在一定条件下整体解的不存在性。     

Finite Travelling Waves for a Semilinear Degenerate Reaction-Diffusion System

In this paper, the existence and nonexistence of finite travelling waves (FTWs) for a semilinear degenerate reaction-diffusion system is studied, where 0 < α _i < 1, m _ij ≥ 0 and ∑ ^N _{j =1} m _ij > 0, i, j = 1,...,N. Necessary and sufficient conditions on existence and large time behaviours of FTWs of (I) are obtained by using the matrix theory, Schauder's fixed point theorem, and upper and lower solutions method. Received July 3, 1997, Revised June 23, 1999, Accepted March 29, 2000     

A nonlocal in time parabolic system whose Fujita critical exponent is not given by scaling

We consider the nonlocal coupled parabolic system

     

非线性边界条件的波动方程的初边值问题

讨论线性波动方程具非线性边界的初边值问题 :utt-△u=0 ,　t >0 ,x∈Ω ,u(0 ,x) =u0 (x) ,　ut(0 ,x) =u1(x) ,　x∈Ω , u γ Ω=g(x) ,　t≥ 0 .通过能量方法和微分、积分不等式技巧 ,研究了解的不稳定性 .     

一类具有混合边界条件的初边值问题解的Blow-up

利用非线性抛物型方程的极大值原理,讨论了一类具有混合边界条件的初边值问题的解的Ｂｌｏｗ－ｕｐ,并得到了Ｂｌｏｗ－ｕｐ时间Ｔ的一个上界。     

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u1=△u 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克分条件,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.     

Some Properties of Solutions for Viscous Cahn-Hilliard Equation

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ，ｗｅｓｔｕｄｙｔｈｅｖｉｓｃｏｕｓＣａｈｎ－Ｈｉｌｉａｒｄｅｑｕａｔｉｏｎｕｔ＋γΔ２ｕ－ｋΔｕｔ＝Δφ（ｕ），（１．１）ｗｈｉｃｈａｒｉｓｅｓｆｒｏｍｍｏｄｅｌｉｎｇｔｈｅｄｙｎａｍｉｃ...     

Blow up for Systems of Wave Equations in Exterior Domain

In this paper the author studies the initial boundary value problem of semilinear wave systems in exterior domain in high dimensions(n ≥ 3). Blow up result is established and what is more, the author gets the upper bound of the lifespan. For this purpose the test function method is used.