共查询到19条相似文献,搜索用时 107 毫秒
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本文研究带有非线性阻尼项的广义Hartree方程的整体适定性:■其中d≥3,a>0,0<α0‖L2≤‖Q‖L2时,我们证明了解是整体存在的;当p=1+2+α/d且q=2+4/d时,我们发现阻尼项可以阻止解的爆破,并进一步研究了解的散射问题. 相似文献
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建立了弱耗散非线性浅水波方程的局部适定性,对于不同的初始值,我们分别得到了解的整体存在性和解的爆破。 相似文献
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本文利用广义凸性方法证明了边界耗散的非线性四阶方程初边值问题整体解的不存在性 相似文献
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通过运用扰动能量方法研究了一类具有弱非线性耗散项粘弹性波方程解的能量衰减性,其中耗散项显依赖于时间t,得到解的衰减率依赖于阻尼的增长速度和t的函数. 相似文献
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针对一类带调和势的耗散非线性schrodinger方程,本文运用一些不等式和先验估计方法研究了其解的行为特征. 相似文献
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LONG-TIME BEHAVIOR OF FINITE DIFFERENCE SOLUTIONS OF THREE-DIMENSIONAL NONLINEAR SCHRODINGER EQUATION WITH WEAKLY DAMPED 总被引:2,自引:0,他引:2
Fa-yongZhang 《计算数学(英文版)》2004,22(4):593-604
The three-dimensional nonlinear SchrSdinger equation with weakly damped that possesses a global attractor are considered. The dynamical properties of the discrete dynamical system which generate by a class of finite difference scheme are analysed. The existence of global attractor is proved for the discrete dynamical system. 相似文献
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This paper is concerned with the Cauchy problem of the nonlinear Hartree equation. By constructing a constrained variational problem, we get a refined Gagliardo–Nirenberg inequality and the best constant for this inequality. We thus derive two conclusions. Firstly, by establishing and analyzing the invariant manifolds, we obtain a new criteria for global existence and blowup of the solutions. Secondly, we get other sufficient condition for global existence with the discussing of the Bootstrap argument. And based on these two conclusions, we also deduce so-called energy-mass control maps, which expose the relationship between the initial data and the solutions. 相似文献
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We prove the existence of an invariant measure for the transition semigroup associated with a nonlinear damped stochastic wave equation in Rn of the Klein--Gordon type. The uniqueness of the invariant measure and the structure of the corresponding Kolmogorov operator are also studied. 相似文献
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Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data 总被引:2,自引:0,他引:2
We consider the defocusing, -critical Hartree equation for the radial data in all dimensions (n5). We show the global well-posedness and scattering results in the energy space. The new ingredient in this paper is that we first take advantage of the term in the localized Morawetz identity to rule out the possibility of energy concentration, instead of the classical Morawetz estimate dependent of the nonlinearity. 相似文献
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曾有栋 《数学物理学报(A辑)》2008,28(4):649-660
该文考虑Rn内在球中和球面系数均有奇异的发展p-Laplac方程的初边值问题的可解性. 在一定条件下证明了轴对称整体解的存在性和不存在性. 相似文献
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Guo Boling 《东北数学》1994,(3)
FiniteDimensionalBehaviorforWeaklyDampedGeneralizedKdV-Burgers EquationsGuoBoling(郭柏灵)(CentreforNonlinearStudies,InstituteofA... 相似文献
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Ji Qiang Zheng 《数学学报(英文版)》2014,30(4):547-566
In this paper,we study the global well-posedness and scattering problem for the energysupercritical Hartree equation iut+Δu.(|x|.γ.|u|2)u=0 with γ4 in dimension d γ.We prove that if the solution u is apriorily bounded in the critical Sobolev space,that is,u ∈Lt∞(I;Hxsc(Rd)) with sc:= γ/2.11,then u is global and scatters.The impetus to consider this problem stems from a series of recent works for the energy-supercritical nonlinear wave equation(NLW) and nonlinear Schrdinger equation(NLS).We utilize the strategy derived from concentration compactness ideas to show that the proof of the global well-posedness and scattering is reduced to disprove the existence of three scenarios:finite time blowup;soliton-like solution and low to high frequency cascade.Making use of the No-waste Duhamel formula,we deduce that the energy of the finite time blow-up solution is zero and so get a contradiction.Finally,we adopt the double Duhamel trick,the interaction Morawetz estimate and interpolation to kill the last two scenarios. 相似文献