非线性波动方程整体解存在的一个必要条件

该文给出了非线性波动方程ｕｎ＝△ｕ＋ｆ（ｕ），（ｆ（ｕ）＝ｕ＾ｐ，ｐ〉１）的Ｃａｕｃｈｙ问题在函数空间Ｃ＾ｋ０（Ｒ＾ｎ）的原点领域有古典整体解的一个必要条件：１／２（ｕ（０）＾２Ｌ２＋ｕｔ（０）＾２Ｌ２）－∫Ｒ＾ｎ∫＾ｕ００ｆ（ｓ）ｄｓｄｘ≤０，并且证明了１〈ｐ〈＾ｎ＾２＋ｎ＋２／ｎ（ｎ－１），ｎ≠１（ｎ＝１，１〈ｐ〈＋∞）古典解与广义解有相同的生命跨度，同时给出了生命跨度的上界估计。     

一类非线性波动方程古典解的存在性

研究了一类非线性波动方程的初边值问题,利用Faedo-Galerkin方法,证明了该初值问题古典解的存在性.     

具有粘性的拟线性波动方程整体解的存在性

首先证明了稳定集的估计,并在一定几何条件下,得到了整体解的存在性。     

一类耦合非线性波动方程全局解的存在性

利用微分不等式和解的延拓原理,研究了一类带非线性阻尼和源项的耦合非线性波动方程,通过分析方程中参数的关系,得到了全局解存在的一些新的充分条件.     

一类非线性波动方程整体解的衰减估计

主要研究一类带有色散项和耗散项的高维非线性波动方程的柯西问题及衰减行为,利用双值分解和Bessel函数的一些性质给出其相应线性方程解的衰减估计,通过压缩映射原理证明了小初值条件下整体解的存在性和衰减估计.     

具耗散项的完全非线性波动方程的经典解

本文利用整体迭代法讨论了具耗散项的完全非线性波动方程具小初值的柯西问题的经典解的存在性及生命跨度的下界估计．     

一类高阶非线性波动型方程整体解的存在性和指数衰减性

研究了一类带有阻尼和源项的高阶非线性波动方程u_(tt)+A+u_t+aAu_t=b|u|~(q-1)u的初边值问题,这里A=(-△)m,m≥1是一个自然数,a≥0,b 0和q1是实数通过构造稳定集证明了这个问题整体解的存在,并应用乘子方法建立了整体解的指数衰减估计同时,在初始能量非负和a=0的条件下,得到了解在有限时间内发生爆破.     

一类具有任意大正初始能量的非线性波动方程整体解的不存在性

研究了一类有限区域上具有阻尼和源项的非线性波动方程的初边值问题,证明了具有任意大正初始能量的整体解的不存在性．     

一类非线性四阶波动方程整体解的存在性

The initial boundary value problem for the fourth-order wave equation utt △2u u=|t|p-1u is considered.The existence and uniqueness of global weak solutions is obtained by using the Galerkin method and the concept of stable set due to Sattinger.     

一类非线性耗散波动方程的渐近性质

本文应用先验估计的方法并结合差分不等式证明了一类非线性耗散波动方程初边值问题整体解的衰减性质。     

Life-span of Classical Solutions to Nonlinear Wave Equations in Two-space-dimensions II

In two-space-dimensional case we get the sharp lower bound of the life-span of classical solutions to the Cauchy problem with small initial data for fully nonlinear wave equations of the form ◻u = F (u, Du, D_zDu) in which F(\hat{λ}) = O(|\hat{λ}|^{1+α}) with α = 2 in a neighbourhood of \hat{λ} = 0. The cases α = 1 and α ≥ 3 have been considered respectively in [1] and [2].     

一维Navier-Stokes方程组整体经典解

本文作者考虑了一维Navier-Stokes方程组Cauchy问题,得到了其经典解的整体光滑可解性。     

一类拟线性波方程的整体光滑解

In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxtt=β(uxn)x, where k>0 and βare real numbers, and n≥2 is an integer. We prove that for any T>0, the Cauchy problem admits a unique global smooth solution u ∈C∞((0, T); H∞(R))∩C ([0, T]; H2(R))∩C1([0, T]; L2(R)) under suitable assumptions on the initial data.     

关于一类具阻尼项的非线性波方程的Cauchy问题

The paper concerns with the existence, uniqueness and nonexistence of global solution to the Cauchy problem for a class of nonlinear wave equations with damping term. It proves that under suitable assumptions on nonlinear the function and initial data the above-mentioned problem admits a unique global solution by Fourier transform method. The sufficient conditions of nonexistence of the global solution to the above-mentioned problem are given by the concavity method.     

Global Solution for Quasilinear Wave Equations with Viscosity and Nonlinear Perturbation

1 IntroductionIn this paper we study globaJ solutions to the initiaLboundary value prob1em for quasilinearwave equations with viscosity and a nonlinear perterbation of the fOrmwhere fl is a bounded domain in RN with smooth boundarY afl, and the norilineax termsa(vp), g(u) axe like a(vp) = (l + )vlP)--'/P(P > 1), g(u) =--ju1"u.This problem describes the motion of fixed membrane with strong viscosity. The globalexistence and stability Of smooth solutions fOr one space dimensional case N = 1…     

三维空间中半线性波动方程组的整体解和自相似解

本文证明了一类半线性波动方程组Cauchy问题整体解的存在唯一性．特别地,证明了自相似解的存在唯一性．同时还得到了渐近自相似解．     

Cauchy Problem for Semilinear Wave Equations in Four Space Dimensions with Small Initial Data

In this paper, we consider the Cauchy problem ◻u(t,x) = |u(t,x)|^p, (t,x) ∈ R^+ × R^4 t = 0 : u = φ(x), u_t = ψ(x), x ∈ R^4 where ◻ = ∂²_t - Σ^4_{i=1}∂²_x_i, is the wave operator, φ, ψ ∈ C^∞_0 (R^4). We prove that for p > 2 the problem has a global solution provided tile initial data is sufficiently small.     

一类耦合非线性方程组的整体解

研究了一类抽象耦合非线性方程组的初值问题,运用Galerkin方法证明了方程整体弱解的存在性,研究对象所在空间均为Hilbert空间.