CONTINUOUS DEPENDENCE ON DATA UNDER THE LIPSCHITZ METRIC FOR THE ROTATION-CAMASSA-HOLM EQUATION

In this article,we consider the Lipschitz metric of conservative weak solutions for the rotation-Camassa-Holm equation.Based on defining a Finsler-type norm on the tangent space for solutions,we first establish the Lipschitz metric for smooth solutions,then by proving the generic regularity result,we extend this metric to general weak solutions.     

非线性Schroedinger方程的整体吸引子

本文讨论了一类带调和势｜x｜^2的非线性Schroedinger方程解的长时间行为，证明了整体吸引子的存在性．     

Blow-up and existence for fast diffusion equations with general nonlinearities

1.IntroductionInthispaperweconsidertheCauchyproblemforthefastdiffusionequationwheremaxandpositivefunction.Thistypeofequationhasbeenextensivelystudiedasamathematicalmodelofalotofphysicalproblems(see[1-3]).Amajortopicofstudyistheexistenceandnonexistenc...     

具有多重非线性的非牛顿多方渗流方程的整体存在性与非存在性

考虑了一个具有多重非线性的抛物模型中,非线性扩散项、非线性反应项和非线性边界流三种非线性机制之间的相互作用.通过构造自相似上解和自相似下解,获得了临界整体存在性曲线和临界Fujita曲线.     

一类带记忆边界条件波动系统解的长时间性态

研究一类带记忆边界条件波动系统解的长时间性态.在初边值满足一定条件时,利用Faedo-Galerkin近似方法得到了系统解的存在唯一性.使用扰动能量方法,证明了系统解的一致衰减性.     

一类超混沌系统解的有界性及其应用

本文研究了在保密通信中有着广泛应用的一类超混沌系统解的界,得到了该类超混沌系统解的界估计表达式.然后将所得到的界估计应用到完全同步之中去, 并做出了相应的数值模拟.     

带非局部阻尼项的粘弹性方程解的衰减估计

In this paper,we consider the following viscoelastic equation u tt- △u +∫t 0 g(t-s)△u(s)ds + a(x)u t + u |u|r = 0 with initial condition and Dirichlet boundary condition.The decay property of the energy function closely depends on the properties of the relaxation function g(t) at infinity.In the previous works of [3,7,11],it was required that the relaxation function g(t) decay exponentially or polynomially as t → +∞.In the recent work of Messaoudi [12,13],it was shown that the energy decays at a similar rate of decay of the relaxation function,which is not necessarily dacaying in a polynomial or exponential fashion.Motivated by [12,13],under some assumptions on g(x),a(x) and r,and by introducing a new perturbed energy,we also prove the similar results for the above equation.     

具梯度源的非散度型抛物方程解的熄灭行为

考虑一类具梯度源项的非散度型抛物方程解的熄灭行为,获得了解的临界熄灭指数,同时,给出了熄灭解的指数衰减估计.     

一类Boussinesq方程解的爆破和不稳定性

研究了一类非线性Boussinesq方程解的爆破和基态解的不稳定性,还得到了问题带在不同域中的初值的整体有界解.