带竞争势的非线性Klein-Gordon方程的稳定集和不稳定集

收稿研究带竞争势的非线性Klein-Gordon方程的柯西问题.首先定义了新的稳定集和不稳定集.其次证明了如果初值进入不稳定集,该柯西问题的解在有限时间内爆破;如果初值进入稳定集,该柯西问题的整体解存在.最后运用势井讨论,我们回答了当初值在什么范围时,该柯西问题的整体解存在这个问题.     

带线性坍塌项和竞争势的非线性波动方程柯西问题的稳定集和不稳定集(英文)

本文考虑带线性坍塌项和竞争势的非线性波动方程柯西问题,定义了新的稳定集和不稳定集,证明了如果初值进入不稳定集,则解在有限时间爆破;如果初值进入稳定集,则整体解存在.运用势井讨论,回答了当初值在多么小的时候,该柯西问题的整体解存在.     

一类耦合非线性Klein-Gordon方程组解的稳定集和不稳定集

利用势井理论的构造方程un-△u u-|v|^ρ 2|u|^ρ△ρu=0;vu-△v v-|u|^ρ＋2|v|^ρv=0的初边值问题的稳定集和不稳定集。证明了当初值属于稳定集时，整体弱解存在，当初值在不稳定集时，解将爆破。     

具阻尼项的非线性波动方程的稳定集与不稳定集

本文利用势井理论讨论一类非线性波动方程的初边值问题 .我们构造其稳定集 W和不稳定集 V,证明了当初值属于 W时 ,对 β∈ R整体弱解存在并且利用乘子法得到当 β>0解的指数衰减估计 ;当初值属于 V时 ,而 β<0时 ,解将爆破     

非线性Klein-Gordon方程整体解存在的最佳条件

本文研究一类带竞争势函数的非线性Klein-Gordon方程的柯西问题.根据基 态的特征,运用势井方法和凹方法导出了该问题解爆破和整体存在的最佳条件. 同时 还回答了当初值为多小时,整体解存在这个问题.     

凸合成模糊对策的模糊稳定集

本建立了凸合成模糊对策的模型，并得到了凸合成模糊对策的模糊稳定集，可由子对策的模糊稳定集表达出来。从而解决了凸合成模糊对策的解的结构问题。     

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。     

一类不连续系统关于闭不变集的有限时间稳定性研究

主要研究右端不连续系统在Filippov解意义下关于闭不变集(未必是紧集)的有限时间稳定问题.当Liapunov函数是Lipschitz连续的正则函数情况下,给出了相关的Liapunov稳定性定理.     

带对数阻尼项的对数型类波方程解的整体存在性与爆破

本文研究一类带对数阻尼项的对数型类波方程的柯西问题,考虑对数阻尼项对解存在性的影响.通过Fourier变换、Laplace变换及Young不等式建立了线性问题解的衰减估计.在恰当的工作空间中,利用整体迭代方法证明了解的整体存在唯一性;利用测试函数方法得到了解的有限时刻爆破.     

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.     

Stable and unstable sets for the Cauchy problem for a nonlinear wave equation with nonlinear damping and source terms

For the Cauchy problem for the nonlinear wave equation with nonlinear damping and source terms we define stable and unstable sets for the initial data. We prove that, if during the evolution the solution enters into the stable set, the solution is global and we are able to estimate the decay rate of the energy. If during the evolution the solution enters into the unstable set, the solution blows up in finite time.     

Existence and uniqueness of global classical solutions to 3D isentropic compressible Navier-Stokes equations with general initial data

In this paper we study the global existence and uniqueness of classical solutions to the Cauchy problem for 3D isentropic compressible Navier-Stokes equations with general initial data which could contain vacuum.We give the relation between the viscosity coefficients and the initial energy,which implies that the Cauchy problem under consideration has a global classical solution.     

Small amplitude solutions of the generalized IMBq equation

In this paper, the global existence of small amplitude solution for the Cauchy problem of the multidimensional generalized IMBq equation is proved. Moreover, we obtain a nonlinear scattering result of the Cauchy problem of the IMBq equation for small initial data.     

具常重特征的非齐次拟线性双曲组的整体弱间断解

This paper considers the Cauchy problem with a kind of non-smooth initial data for general inhomogeneous quasilinear hyperbolic systems with characteristics with constant multiplicity. Under the matching condition, based on the refined fomulas on the decomposition of waves, we obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution to the Cauchy problem.     

Global well-posedness for the viscous shallow water system with Korteweg type

In this paper, we study the Cauchy problem for a viscous shallow water system with Korteweg type in Sobolev spaces. We first establish the local well-posedness of the solution by using the Friedrich method and compactness arguments. Then, we prove the global existence of the solution to the system for the small initial data.     

Global existence,singular solutions,and ill‐posedness for the Muskat problem

The Muskat, or Muskat‐Leibenzon, problem describes the evolution of the interface between two immiscible fluids in a porous medium or Hele‐Shaw cell under applied pressure gradients or fluid injection/extraction. In contrast to the Hele‐Shaw problem (the one‐phase version of the Muskat problem), there are few nontrivial exact solutions or analytic results for the Muskat problem. For the stable, forward Muskat problem, in which the higher‐viscosity fluid expands into the lower‐viscosity fluid, we show global‐in‐time existence for initial data that is a small perturbation of a flat interface. The initial data in this result may contain weak (e.g., curvature) singularities. For the unstable, backward problem, in which the higher‐viscosity fluid contracts, we construct singular solutions that start off with smooth initial data but develop a point of infinite curvature at finite time. © 2004 Wiley Periodicals, Inc.     

Temps de vie des solutions d'un problème de Cauchy non linéaire

We solve the global Cauchy problem, with small initial data, in the space of the holomorphic functions with respect to t and Gevrey class with respect to x. We establish the existence and the stability of the solution to Cauchy problem with nul initial data without hyperbolicity hypothesis. In the stationary case, we give estimates of life span of the solutions with respect to size of the initial data.     

Global existence of smooth solutions to two-dimensional compressible isentropic Euler equations for Chaplygin gases

In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.