共查询到19条相似文献,搜索用时 89 毫秒
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研究了一类含双参数的非线性高阶微分方程的奇摄动问题.运用合成展开法构造了问题的形式渐近解,并运用微分不等式理论证明了原问题解的存在性及所得形式渐近解的一致有效性. 相似文献
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运用合成展开法和微分不等式理论研究了一类四阶方程的奇摄动边值问题.先运用合成展开法,构造了问题的形式渐近解,再运用微分不等式理论证明了原问题解的存在性及所得形式渐近解的一致有效性.最后用一个例子来说明所得结果的意义. 相似文献
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研究了一类具非线性边值条件的非线性方程的奇摄动问题,运用合成展开法构造了问题的形式渐近解,并用微分不等式理论证明了所得渐近解的一致有效性. 相似文献
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运用合成展开法,构造了一类具非线性边值条件的双参数奇摄动问题的形式渐近解,并利用微分不等式理论,证明了该问题解的存在性和渐近解的一致有效性. 相似文献
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该文研究了具有快慢层的非光滑奇异摄动问题的空间对照结构.利用边界层函数法构造了该问题的形式渐近解,并运用"缝接法"证明了问题光滑解的存在性以及渐近解的一致有效性.最后,通过例子验证了所得结果的有效性. 相似文献
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研究了一类非线性高阶微分方程的奇摄动问题.运用合成展开法构造了问题的形式渐进解,并运用了微分不等式理论证明了原问题解的存在性及所得形式渐近解的一致有效性,最后给出了一个例子说明结果的意义. 相似文献
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本文研究带慢变量的右边不连续的拟线性奇异摄动方程组的空间对照结构.利用边界层函数法构造了该方程组的形式渐近解,并运用"缝接法"证明问题解的存在性以及渐近解的一致有效性.最后,通过例子验证了所得结果的有效性. 相似文献
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通过引入伸展变量和非常规的渐近序列{∈}),运用合成展开法,对一类具非线性边界条件的非线性高阶微分方程的奇摄动问题构造了形式渐近解,再运用微分不等式理论证明了原问题解的存在性及所得渐近近似式的一致有效性. 相似文献
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讨论了一类具有超抛物型方程的反应扩散问题.首先,证明了比较定理.其次,构造了形式渐近解.然后,利用微分不等式方法,研究了问题解的存在、唯一性和渐近性态.最后得到了原问题解的渐近展开式. 相似文献
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利用三重尺度方法对一类小周期椭圆方程进行了三重尺度渐近展开分析,构造了对应的三重尺度形式渐近展开式,得到了均匀化常数和均匀化方程.在形式渐近展开的基础上,构造了对应边值问题解的三重尺度渐近近似解,并分析了对应三重尺度形式渐近误差估计. 相似文献
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A system of equations that arises in a singularly perturbed optimal control problem is studied. We give conditions under which a formal asymptotic solution exists. This formal asymptotic solution consists of an outer expansion and left and right boundary-layer expansions. A feature of our procedure is that we do nota priori eliminate the control function from the problem. In particular, we construct a formal asymptotic expansion for the control directly. We apply our procedure to a Mayer-type problem. The paper concludes with a worked example. 相似文献
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Cheng Ouyang 《分析论及其应用》2005,21(4):311-316
A class of semi-linear Robin problem is considered. Under appropriate assumptions, the existence and asymptotic behavior of its solution are studied more carefully. Using stretched variables, the formal asymptotic expansion of solution for the problem is constructed and the uniform validity of the solution is obtained by using the method of upper and lower solution. 相似文献
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This article solved the asymptotic solution of a singularly perturbed boundary value problem with second order turning point, encountered in the dissipative equilibrium vector field of the coupled convection disturbance kinetic equations under the constrained filed and the gravity. Using the matching of asymptotic expansions, the formal asymptotic solution is constructed. By using the theory of differential inequality the uniform validity of the asymptotic expansion for the solution is proved. 相似文献
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The Hamiltonian boundary-value problem, associated with a singularly-perturbed linear-quadratic optimal control problem with delay in the state variables, is considered. A formal asymptotic solution of this boundary-value problem is constructed by application of the boundary function method. The justification of this asymptotic solution is done. The asymptotic solution of the Hamiltonian boundary-value problem is constructed and justified assuming boundary-layer stabilizability and detectability. 相似文献
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研究了一类两参数非线性反应扩散积分微分奇摄动问题.利用奇摄动方法,构造了问题的外部解、内部激波层、边界层及初始层校正项,由此得到了问题解的形式渐近展开式.最后利用积分微分方程的比较定理证明了该问题解的渐近展开式的一致有效性. 相似文献
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Liu Shude Mo Jiaqi Chen Xiu Dept. of Math. Physics Hefei University Hefei ) 《Annals of Differential Equations》2008,(4):407-412
In this paper, we consider the solvability for a singularly perturbed Robin problem of semi-linear differential system. Using the boundary layer corrective method, the formal asymptotic solution is constructed. Finally, the uniform validity of such asymptotic expansions solution is proved. 相似文献
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Yao Jingsun~ Chen Lihua~ Mo Jiaqi~ 《Annals of Differential Equations》2007,23(3):358-364
The solvability for the nonlinear singularly perturbed boundary value pro- blem of differential system is considered.Using the boundary layer corrective method the formal asymptotic solution is constructed.And using the theory of differential inequality proves the uniform validity of the asymptotic expansion for the solution. 相似文献