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.     

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。     

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．     

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。     

关于具有偏差变元的双曲方程解的强迫振动性

关于具有偏差变元的双曲方程解的强迫振动性俞元洪崔宝同（中国科学院应用数学研究所，北京１０００８０）（山东滨州师范专科学校，滨州２５６６０４）ＯＮＴＨＥＦＯＲＣＥＤＯＳＣＩＬＬＡＴＩＯＮＳＯＦＳＯＬＵＴＩＯＮＳＯＦＨＹＰＥＲＢＯＬＩＣＥＱＵＡＴＩＯＮＳ...     

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。     

一类非线性退化波动方程解的爆破

考虑了有界区域上一类非线性退化波动方程的初边值问题.通过改进Vitillaro,Li和Tsai的方法,建立了非正的初始能量以及正的初始能量下解的爆破结果.同时,还给出了解的生命跨度估计.     

Life span of positive solutions for a semilinear heat equation with general non-decaying initial data

We prove upper bounds on the life span of positive solutions for a semilinear heat equation. For non-decaying initial data, it is well known that the solutions blow up in finite time. We give two types estimates of the life span in terms of the limiting values of the initial data in space.     

一类Boussinesq型方程整体解的存在性和唯一性

证明一类6阶Boussinesq型方程Cauchy问题整体广义解和整体古典解的存在性和唯一性,给出解在有限时刻发生爆破的充分条件.     

Local existence and global nonexistence theorems for a damped nonlinear hyperbolic equation

The existence and uniqueness of the local generalized solution to the initial boundary value problem for the three-dimensional damped nonlinear hyperbolic equation

     

Estimates for a solution to one differential inequality

In a domain D = Ω × (?T,T) we consider a differential inequality whose left-hand side contains a linear second-order hyperbolic operator with coefficients depending only on x ∈ ? ⁿ, n ≥ 2, and the right-hand side contains the modulus of the gradient of the sought function. We supplement the inequality with the Cauchy data on the lateral part of the boundary of D and consider the problem of estimating a solution to the differential inequality satisfying the Cauchy data. We establish the estimate under some assumptions that involves the upper bound of the sectional curvatures of the Riemannian space associated with the differential operator, the Riemannian diameter of Ω, and the length of the interval (?T,T). The result is generalized to the case of compact domains bounded from above and below by characteristic surfaces.