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具耗散项的绝热气动力学方程组的整体光滑解 总被引:1,自引:0,他引:1
郑永树 《数学年刊A辑(中文版)》1996,(2)
考虑拉格朗日坐标下具耗散项的绝热气动力学方程组的初值问题,分别证明了其整体光滑解的存在性与非存在性. 相似文献
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本文利用KDV方程所对应的线性方程解所具有的光滑效应及压缩映像原理,得到了Hirota-Satsuma系统初值问题的局部和整体适定性结果. 相似文献
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本文讨论一类具非线性二阶导数项的Schr(?)dinger方程,它在物理上描述了上混合振荡传播.根据基态的变分特征,运用势井方法和凹方法,我们获得了其初值问题整体解存在的一个最佳条件,另外还证明了当初值多小时,初值问题的整体解存在. 相似文献
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本文用积分估计和不动点原理证明了一类广义Kuramoto-Sivashinsky型方程初值问题光滑整体解的存在唯一性,并在不同情况下讨论了解的破裂性,并给出了导致破裂性的充分条件. 相似文献
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讨论具有非线性耗散项双曲系统的初值问题,对初值的模不加小性假设,而要求其一阶导数适当小情形下,证明其光滑解的整体存在性,并用经典解的特征线法获得解的模估计,同时应用极值原理得到解的偏导数的一致估计. 相似文献
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本文讨论一类具非线性二阶导数项的Schrodinger方程,它在物理上描述了上混合振荡传播.根据基态的变分特征,运用势井方法和凹方法,我们获得了其初值问题整体解存在的一个最佳条件,另外还证明了当初值多小时,初值问题的整体解存在. 相似文献
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考虑方程其中a,b为任意实常数,τ为正常数.本文在复数域上求得了方程(*)全部根的精确分布.在文[1]和[2]中应用Laplace变换法,得到了滞后型方程初值问题的形式解公式下:其中x(t)为初值问题的解,这里H(θ)为Heaviside函数.方程(*)为初值问题(E)中方程的特征方程.应用本文结果于形式解公式(1.1),可求得初值问题(E)的精确解.篇幅所限,此问题另文讨论. 相似文献
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In this article,we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional(m-D) conservation law with unbounded initial value;our methods are new and essentially different with the situation of bounded initial value. 相似文献
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Li Chen Ling Hsiao Gerald Warnecke 《应用数学学报(英文版)》2007,23(1):9-28
This paper considers a kind of strongly coupled cross diffusion parabolic system,which can be usedas the multi-dimensional Lyumkis energy transport model in semiconductor science.The global existence andlarge time behavior are obtained for smooth solution to the initial boundary value problem.When the initialdata are a small perturbation of an isothermal stationary solution,the smooth solution of the problem under theinsulating boundary condition,converges to that stationary solution exponentially fast as time goes to infinity. 相似文献
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Global Existence and Asymptotic Behavior of the Solution to 1-D Energy Transport Model for Semiconductors
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In this paper, we study the asymptotic behavior of global smooth solution to the initial boundary problem for the 1-D energy transport model in semiconductor science. We prove that the smooth solution of the problem converges to a stationary solution exponentially fast as t → ∞ when the initial data is a small perturbation of the stationary solution. 相似文献
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The existence of global smooth solutions for a nonlinear 5th order equation of KdV type with the periodic boundary condition and initial value condition is proved, we also get the local smooth characterization of the solution for the initial value problem. 相似文献
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Jiaqing Pan 《Journal of Mathematical Analysis and Applications》2007,325(1):703-714
In this paper, the existence, uniqueness and dependence on initial value of solution for a singular diffusion equation with nonlinear boundary condition are discussed. It is proved that there exists a unique global smooth solution which depends on initial data in L1 continuously. 相似文献
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We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (?1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest. 相似文献
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Mitchell Luskin 《Journal of Mathematical Analysis and Applications》1981,84(2):614-630
We model the flow of a fluid in a pipe by a first-order nonlinear hyperbolic system with zero-order nonlinear dissipation. We prove that a unique, global smooth solution exists if the initial data are in an appropriate invariant region and if the first derivatives of the initial data are sufficiently small. 相似文献
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Daoguo Zhou 《Applicable analysis》2017,96(6):1004-1015
We consider a mathematical model for an incompressible Newtonian fluid with intrinsic degrees of freedom in a smooth bounded domain. We first show that there exists a unique local strong solution for large initial data. Then, we prove that the local strong solution is indeed global provided that the initial data is sufficiently small. Furthermore, we prove that when the strong solution exists, all the global weak solutions constructed by Lions must be equal to the unique strong solution with the same initial data. 相似文献
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The paper deals with the existence and uniqueness of smooth solution for a generalized Zakharov equation. We establish local in time existence and uniqueness in the case of dimension d=2,3. Moreover, by using the conservation laws and Brezis-Gallouet inequality, the solution can be extended globally in time in two dimensional case for small initial data. Besides, we also prove global existence of smooth solution in one spatial dimension without any small assumption for initial data. 相似文献
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Bo-Ling Guo & Xiang-Hui Wu 《计算数学(英文版)》1991,9(4):330-336
A spectral method is proposed, the existence and uniqueness of the global and smooth solution are proved for the periodic initial value problem of the generalized K-S equation. The error estimates are established and the convergence is proved for the approximate solution of the spectral method. 相似文献