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讨论了完备Brouwer格上有限inf-αT(其中T为伪t-模)合成关系方程,给出了方程解集非空的充要条件.当方程infαTj∈J(αj,xj)=b中b为交既约元时,证明了方程解集中存在极大解的一个充分条件,并给出了方程解集的结构. 相似文献
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拓扑度理论是研究非线性算子方程解的存在性的有力工具.利用拓扑度的方法,对Z-P-S空间中一类非线性算子方程解的存在性问题进行了研究,得到了若干新的结果. 相似文献
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奇异积分方程解的一种稳定性 总被引:2,自引:1,他引:1
许永甲 《数学物理学报(A辑)》1991,11(4):448-456
本文讨论了区间[-1,1]上带Cauchy核的奇异积分方程解的稳定性,给出了这类方程的一种稳定性条件,获得了扰动方程解的估计,证明了方程解对于已知函数的连续依赖性。 相似文献
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许多作者研究了复差分方程解的存在性及增长性问题,得到了较多理想的结果.本文利用亚纯函数Nevanlinna值分布理论,研究了一类复高阶非线性差分方程解的表达式问题,将复差分方程的一结果推广至复差分方程组中. 相似文献
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研究了Banach空间中定义在无穷区间R+上具有无穷多个脉冲点的Hammerstein积分方程解的存在性.利用MLnch不动点定理,建立了该类方程解的存在定理,并给出实例说明了该定理在无穷维脉冲积分方程组中的应用. 相似文献
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一类非线性波动方程的显式精确解 总被引:14,自引:0,他引:14
本文用直接方法和假设的一种结合求出了一类较广泛的非线性波动方程utt-a1uxx+a2ut+a3u+a4uS^2+a5u^3=0的一些显式精确行波解,贱个有重要的非线性数学物理方程,如φ^4方程,Klein-Gordon方程,Sine-Gordon方程,及Sinh-Gordon方程的近似,Landau-Ginzburg-Higgs方程,Duffing方程,非线性电报方程等都可作为该方程的特殊情形得 相似文献
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Wei-jun Tang Hong-yuan Fu Long-jun Shen 《计算数学(英文版)》2001,19(5):489-500
1. IntroductiouThe mathewtical tratod of the scattering Of theharmonic acoustic or electromagnoticwaves by an Mtely lOng sethecylindrical obstacle with a 8mooth opeu coDtour crewSeCtboF C Rs Ieads to unbounded boundare wtue problems for the Helmhltz equabo I3lwith wave nUmer h > 0.In the singtelayer Woach one Seeks the solutbo in the formwhere d8. is the element of arc length, and the fundamental solUbo to the Helmholtz equatfonis giveu byin terms Of the Hds fUnction H6') of order zero… 相似文献
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In this paper, we propose complete radiation boundary conditions (CRBCs) for solutions of the convected Helmholtz equation with a uniform mean flow in a waveguide. We first study CRBCs for the Helmholtz equation in a waveguide. Noting that the convected Helmholtz equation is associated with the Helmholtz equation via the Prandtl–Glauert transformation, CRBCs for the convected Helmholtz equation is derived from CRBCs for the Helmholtz equation. We analyse well-posedness and convergence of approximate solutions satisfying CRBCs for the convected Helmholtz equation. In addition, simple numerical experiments will be presented to confirm the theoretical results. 相似文献
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Master equations of different types describe the evolution (reduced dynamics) of a subsystem of a larger system generated
by the dynamic of the latter system. Since, in some cases, the (exact) master equations are relatively complicated, there
exist numerous approximations for such equations, which are also called master equations.
In the paper, we develop an exact master equation describing the reduced dynamics of the Wigner function for quantum systems
obtained by a quantization of a Hamiltonian system with a quadratic Hamilton function. First, we consider an exact master
equation for first integrals of ordinary differential equations in infinite-dimensional locally convex spaces. After this,
we apply the results obtained to develop an exact master equation corresponding to a Liouville-type equation (which is the
equation for first integrals of the (system of) Hamilton equation(s)); the latter master equation is called the master Liouville
equation; it is a linear first-order differential equation with respect to a function of real variables taking values in a
space of functions on the phase space. If the Hamilton equation generating the Liouville equation is linear, then the vector
fields that define the first-order linear differential operators in the master Liouville equations are also linear, which
in turn implies that for a Gaussian reference state the Fourier transform of a solution of the master Liouville equation also
satisfies a linear differential equation.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 5, pp. 203–219, 2005. 相似文献
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本文讨论了能量方程是压力一密度关系的一维半导体流体动力学模型方程,通过把欧拉-泊松方程变成拟线性波动方程,利用拟线性波动方程的局部解存在性,得到一维半导体流体动力学模型的局部解,并且解是有界的。 相似文献
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Lijun Zhang Jianming Zhang Yuzhen Bai Robert Hakl 《Journal of Applied Analysis & Computation》2019,9(5):1987-1998
The singular traveling wave solutions of a general 4-parameter family equation which unifies the Camass-Holm equation, the Degasperis-Procesi equation and the Novikov equation are investigated in this paper. At first, we obtain the explicit peakon solutions for one of its specific case that $a=(p+2)c$, $b=(p+1)c$ and $c=1$, which is referred to a generalized Camassa-Holm-Novikov (CHN) equation, by reducing it to a second-order ordinary differential equation (ODE) and solving its associated first-order integrable ODE. By observing the characteristics of peakon solutions to the CHN equation, we construct the peakon solutions for the general 4-parameter breaking wave equation. It reveals that singularities of the peakon solutions come up only when the solutions attain singular points of the equation, which might be a universal principal for all singular traveling wave solutions for wave breaking equations. 相似文献
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Aly R. Seadawy 《Applied Mathematics Letters》2012,25(4):687-691
In the present study, we converted the resulting nonlinear equation for the evolution of weakly nonlinear hydrodynamic disturbances on a static cosmological background with self-focusing in a two-dimensional nonlinear Schrödinger (NLS) equation. Applying the function transformation method, the NLS equation was transformed to an ordinary differential equation, which depended only on one function ξ and can be solved. The general solution of the latter equation in ζ leads to a general solution of NLS equation. A new set of exact solutions for the two-dimensional NLS equation is obtained. 相似文献
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Mohamed Hayek 《Applied mathematics and computation》2011,218(6):2407-2420
Based on the simplest equation method, we propose exact and traveling-wave solutions for a nonlinear convection-diffusion-reaction equation with power law nonlinearity. Such equation can be considered as a generalization of the Fisher equation and other well-known convection-diffusion-reaction equations. Two important cases are considered. The case of density-independent diffusion and the case of density-dependent diffusion. When the parameters of the equation are constant, the Bernoulli equation is used as the simplest equation. This leads to new traveling-wave solutions. Moreover, some wavefront solutions can be derived from the traveling-wave ones. The case of time-dependent velocity in the convection term is studied also. We derive exact solutions of the equations by using the Riccati equation as simplest equation. The exact and traveling-wave solutions presented in this paper can be used to explain many biological and physical phenomena. 相似文献
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Comparison theorems for the initial value finite domain one dimensional heat equation with a discontinuous forcing term are extended to a coupled system of a heat equation and an ordinary differential equation in space, rather than the usual ordinary differential equation in time, that arises in combustion theory. 相似文献
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Y. Fujita 《Applied Mathematics and Optimization》2001,43(2):169-186
In this paper we consider the Bellman equation in a one-dimensional ergodic control. Our aim is to show the existence and
the uniqueness of its solution under general assumptions. For this purpose we introduce an auxiliary equation whose solution
gives the invariant measure of the diffusion corresponding to an optimal control. Using this solution, we construct a solution
to the Bellman equation. Our method of using this auxiliary equation has two advantages in the one-dimensional case. First,
we can solve the Bellman equation under general assumptions. Second, this auxiliary equation gives an optimal Markov control
explicitly in many examples. \keywords{Bellman equation, Auxiliary equation, Ergodic control.}
\amsclass{49L20, 35G20, 93E20.}
Accepted 11 September 2000. Online publication 16 January 2001. 相似文献