共查询到18条相似文献,搜索用时 234 毫秒
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讨论了一类有界区域上具有有色噪声干扰的随机Burgers方程奇摄动解,其波动率服从弱噪声Ornstein-Uhlenbeck(O-U)过程.由波运动的转移概率密度函数满足的后向Kolmogorov方程,得到随机Burgers的期望所满足的后向Kolmogorov方程.由于期望满足的后向Kolmogorov方程的初边值问题条件涉及到一类确定性Burgers方程的解,因此该问题实际上是Burgers方程和Kolmogorov方程的联立形式.首先,应用奇摄动方法,对一类确定性Burgers方程进行了正则渐近展开,由Schauder估计、Ascoli-Arzela定理证明了非线性抛物方程渐近解的有界性与存在性,由Lax-Milgram定理证明了线性抛物方程渐近解的有界性与存在性,得到波速率的形式渐近解.其次,由奇摄动理论,对期望满足的方程进行了奇摄动渐近展开和边界层矫正,由二阶线性偏微分方程理论,得到边界层函数渐近解存在且有界.应用极值原理、De-Giorgi迭代技术分别证明了波速率和波期望渐近解的余项有界,得到渐近解的一致有效性. 相似文献
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讨论了一类超抛物型方程的非线性奇摄动问题.首先引入了相应问题的比较定理,然后利用奇摄动方法构造了问题的形式渐近解,最后利用比较定理,证明了问题广义解的存在性及其渐近性态. 相似文献
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利用Lyapunov-Schmidt方法证明了带有一阶导数项和(V)α势函数的非线性Schrodinger方程半经典孤波解的存在性及其集中性质.
具体地讲,当相当于Planck常数的奇摄动参数趋于零时,证明了该非线性Schrodinger方程的孤波解存在并且这些解在其势函数的非退化临界点处集中.
研究的是椭圆型方程的奇摄动问题,方程带有一阶导数项是本文特征之一. 相似文献
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唐荣荣 《数学物理学报(A辑)》2008,28(3):546-552
利用渐近理论,讨论了一类具有边界摄动的奇摄动问题.在适当的条件下,得出了这类问题解的存在性条件及其渐近解, 并将所得的结果应用于一类壁面波的传播问题. 相似文献
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研究不满足法向双曲条件的二阶半线性非自治奇摄动Dirichlet边值问题.首先,利用边界层函数法,构造了问题在两个区间端点的代数边界层,获得了形式渐近解;接着,利用上下解方法,证明了解的存在性、渐近解的一致有效性以及渐近解与精确解之间的误差估计.研究表明:通过对奇异摄动参数进行适当的尺度变换,一定条件下可处理任意退化的二阶半线性非自治奇摄动边值问题.最后,通过一个典型例子验证了理论结果的正确性. 相似文献
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应用非Fourier热传导定律构建了单层材料中温度场模型,即一类在无界域上带小参数的奇摄动双曲方程,通过奇摄动展开方法,得到了该问题的渐近解.首先应用奇摄动方法得到了该问题的外解和边界层矫正项,通过对内解和外解的最大模估计和关于时间导数的最大模估计以及线性抛物方程理论,得到了内外解的存在唯一性,从而得到了解的形式渐近展开式.通过余项估计,给出了渐近解的L2估计,得到了渐近解的一致有效性,从而得到了无界域上温度场的分布.通过奇摄动分析,给出了非Fourier 温度场与Fourier 温度场的关系,描述了非Fourier温度场的具体形态. 相似文献
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研究一类具有不连续系数的奇异摄动二阶拟线性边值问题,其解因一阶导数的不连续性而出现内部层.用合成展开法和上下解定理得到所提问题内部层解的存在性和渐近估计.所得结果应用到由Farrell等(Farrell P A,O'Riordan E,Shishkin G.A class of singularly perturbed quasilineax differential equations with interiors layers.Mathematics of Computation,2009,78:103-127)所提出的一个特殊拟线性问题. 相似文献
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T. A. Mel'nik 《Ukrainian Mathematical Journal》1994,46(11):1660-1666
We construct the asymptotic expansion of a solution of the Cauchy problem for a singularly perturbed system of differential equations whose right-hand side is discontinuous on a certain surface. We consider the case where the surface of discontinuity is crossed and estimate the remainder of the constructed asymptotic expansion.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 11, pp. 1502–1508, November, 1994.The present work was supported by the Ukrainian State Committee on Science and Technology. 相似文献
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In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method. 相似文献
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We construct asymptotic solutions of a singularly perturbed system of integro-differential equations in which the matrix coefficient of the derivative is degenerate at a point. 相似文献
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This work is concerned with asymptotic properties of solutions to forward equations for singularly perturbed Markov chains with two small parameters. It is motivated by the model of a cost-minimizing firm involving production planning and capacity expansion and a two-level hierarchical decomposition. Our effort focuses on obtaining asymptotic expansions of the solutions to the forward equation. Different from previous work on singularly perturbed Markov chains, the inner expansion terms are constructed by solving certain partial differential equations. The methods of undetermined coefficients are used. The error bound is obtained. 相似文献
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林苏榕 《数学物理学报(A辑)》2007,27(6):1133-1140
该文研究向量二阶非线性积分微分方程边值问题的奇摄动, 在适当的条件下利用对角化方法证明了解的存在性, 构造出解的渐近展式并给出余项的一致有效的估计. 相似文献
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V. A. Beloshapko V. F. Butuzov 《Computational Mathematics and Mathematical Physics》2013,53(8):1117-1127
The solution of a singularly perturbed elliptic boundary value problem is constructed, and an asymptotic expansion of the boundary-layer solution in the case of a double root of the degenerate equation is justified. The multiplicity of the root leads to a qualitative change in the asymptotic representation of the solution as compared with the case of a simple root. 相似文献
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We construct an asymptotic expansion for solutions to nonlinear singularly perturbed systems of impulsive differential equations. We successively determine all terms of the asymptotic expansion by means of pseudoinverse matrices and orthoprojections. 相似文献