两参数非局部非线性反应扩散Robin问题的渐近解

研究了一类两参数非局部反应扩散奇摄动Robin问题.利用奇摄动方法,对该问题解的结构在两个小参数相互关联的情形下作了讨论.得到了该问题的渐近解.     

一类两参数半线性奇摄动问题解的渐近性态

本文研究了一类两参数半线性奇摄动问题的基本模型.利用奇摄动方法,对该问题解的结构在两个小参数相互关联的三种不同情形下作了讨论.得到了该问题在三种不同情形下的渐近解并证明了在三种情形下解的结构与渐近性态.     

一类两参数非线性奇摄动边值问题解的渐近性态

本文研究了一类两参数非线性奇摄动边值问题的基本模型.利用奇摄动方法,对该问题解的结构在两个小参数相互关联的三种不同情形下作了讨论,得到了该问题的渐近解并证明了在三种情形下不同的解的结构与渐近性态.     

两参数非线性反应扩散积分微分方程的内层激波渐近解

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.     

一类四阶方程两参数的奇摄动问题

研究了一类四阶方程两参数的奇摄动问题.利用奇摄动方法,对该同题的解的结构在两个小参数相互关联的三种不同情形下作了全面的彻底的讨论.得到了该问题在三种不同情形下的渐近解;证明了在三种情形下完全不同的解的结构与极限性态;给出了比较完善的结果.     

非Fourier温度场分布的奇摄动解

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.     

两参数非线性发展方程的奇摄动尖层解

本文研究了一类具有非线性发展方程奇摄动问题.引入伸长变量和多重尺度,构造了初始边值问题外部解和尖层、边界层和初始层校正项,得到了问题形式解.利用不动点定理,证明了问题的解的一致有效性.推广了对两参数的奇摄动问题的研究结果.     

一类双参数非线性高阶反应扩散方程的摄动解法

研究了一类两参数非线性反应扩散奇摄动问题的模型.利用奇摄动方法,对该问题解的结构在两个小参数相互关联的情形下作了讨论.首先,构造问题的外部解; 之后在区域的边界邻域构造局部坐标系,再在该邻域中引入多尺度变量,得到问题解的边界层校正项; 然后引入伸长变量,构造初始层校正项,并得到问题解的形式渐近展开式;最后建立了微分不等式理论,并由此证明了问题的解的一致有效的渐近展开式.用上述方法得到的各次近似解,具有便于求解、精度高等特点.     

两参数非线性发展方程的奇摄动尖层解（英文）

本文研究了一类具有非线性发展方程奇摄动问题.引入伸长变量和多重尺度,构造了初始边值问题外部解和尖层、边界层和初始层校正项,得到了问题形式解.利用不动点定理,证明了问题的解的一致有效性.推广了对两参数的奇摄动问题的研究结果.     

一类热传导系数跳跃的非Fourier温度场分布的奇摄动双参数解

应用非Fourier热传导定律构建了温度场模型,即一类在有界域上带小参数的奇摄动双曲方程,由于温度急剧变化热传导系数出现跳跃的情况,得到了非线性的具有间断系数的奇摄动双参数双曲方程.通过奇摄动双参数展开方法,得到了该问题的渐近解;其次对热传导系数跳跃位置进行了定性分析,得到了确定热传导系数跳跃位置的计算公式,从而确定了解的形式渐近展开式;再通过余项估计,得到了渐近解的一致有效性,从而得到了完整温度场的分布.     

两参数奇异摄动非线性双曲型微分系统的过渡冲击层广义解

研究了一类两参数双曲型微分系统奇异摄动初始边值问题.首先,利用奇异摄动理论和方法,注意到两个小参数,构造了问题的外部解.其次,利用多重尺度变量和伸长变量,分别得到了原问题解的过渡冲击层、边界层和初始层校正项.最后,得到了原问题解的渐近展开式,并利用泛函分析不动点理论,证明了渐近解的一致有效性.由本方法求得的原问题的渐近解,它还可以进行微分,积分等解析运算,从而能了解相应过渡冲击层解的更进一步的性态.因此本方法具有良好的应用前景.     

一类双参数三阶半线性方程边值问题的奇摄动

研究一类双参数三阶半线性方程边值问题的奇摄动，讨论了摄动解随两参数的不同量级所呈现的不同性态的边界层现象，并给出了解的一致有效的渐近展开式．     

具有双参数的弱非线性方程的奇摄动解

讨论了一四阶具有双参数的弱非线性方程在有限区间上的奇摄动边值问题．在一定的假设下,首先,利用幂级数形式展开方法,构造了原问题的外部解A·D2其次,利用伸长变量,在左端点附近构造问题解的第一边界层校正项．然后,利用更强的伸长变量,仍然在左端点附近构造问题解的第二边界层校正项．第二边界层的厚度比第一边界层的厚度更小,形成在左端点附近的边界层的套层．最后利用微分不等式理论,证明了边值问题解的存在性、和在整个区间内一致有效性和渐近性态,得到了满意的结果．     

Plastic flow of an axisymmetric layer under an end load

A solution is constructed for the problem of the stress state of a thin plastic axisymmetric layer subjected to an end load and compression between rigid slabs. The unknown parameters in the solution are determined from two integral equations. A numerical study is made of the range of compressive loads for which plastic flow occurs. The components of the stresses in the layer are also determined.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 106–110, 1988.     

Contact problem for a layer with two stamps : PMM vol. 42, no. 6, 1978, pp. 1068–1073

A problem of impressing coaxial stamps of circular cross section into the upper and lower surface of a homogeneous elastic layer is studied. The bases of the stamps have axial symmetry. The parts of the layer surfaces lying oustide the contact zone are stress-free, there is no friction or coupling between the layer and the stamps. A system of two integral equations with two unknown functions is obtained, and provides a solution of the problem. The method of separating the singularities provides the way of reducing this system to the Fredholm equations of second kind. An approximate solution of the equations is obtained for the case of flat stamps under the assumptions that the two parameters entering the system are sufficiently small.

Problems of a layer with various boundary conditions were formulated and solved in many papers and books, e.g. [1, 2]. However, to the best of the author's knowledge, in all these problems the conditions at the boundary were assumed different only on one side of the layer; in the present problem the boundary conditions are mixed at both sides of the layer, and this results in a system of two integral equations.     

MULTIPLE BOUNDARY LAYER PHENOMENA OF SOLUTION OF BOUNDARY VALUE PROBLEM FOR THIRD ORDER DIFFERENTIAL EQUATION WITH TWO PARAMETERS

1IntroductionAlotofworkonthesingularlyperturbedboundaryvalueproblemofthirdorderdifferentialequationwereinthecasesofonesmallparameter[1-3].Inthispaper9wediscussthe8ingularperturbationofboundaryvalueproblemforathirdordersemilinearordinarydifferentialequatio…     

Theory of the hypersonic viscous shock layer at high Reynolds numbers and intensive injection of foreign gases : PMM vol. 38, n 6, 1974, pp. 1015–1024

The hypersonic flow around smooth blunted bodies in the presence of intensive injection from the surface of these is considered. Using the method of external and internal expansions the asymptotics of the Navier-Stokes equations is constructed for high Reynolds numbers determined by parameters of the oncoming stream and of the injected gas. The flow in the shock layer falls into three characteristic regions. In regions adjacent to the body surface and the shock wave the effects associated with molecular transport are insignificant, while in the intermediate region they predominate. In the derivation of solution in the first two regions the surface of contact discontinuity is substituted for the region of molecular transport (external problem). An analytic solution of the external problem is obtained for small values of parameters ₁ = ρ_∞/ρs^* and δ = ρ_ω^*1/2ν_ω^*/ρ_∞1/2ν_∞, in the form of corresponding series expansions in these parameters. Asymptotic formulas are presented for velocity profiles, temperatures, and constituent concentration across the shock layer and, also, the shape of the contact discontinuity and of shock wave separation. The derived solution is compared with numerical solutions obtained by other authors. The flow in the region of molecular transport is defined by equations of the boundary layer with asymptotic conditions at plus and minus infinity, determined by the external solution (internal problem). A numerical solution of the internal problem is obtained taking into consideration multicomponent diffusion and heat exchange. The problem of multicomponent gas flow in the shock layer close to the stagnation line was previously considered in [1] with the use of simplified Navier-6tokes equations.The supersonic flow of a homogeneous inviscid and non-heat-conducting gas around blunted bodies in the presence of subsonic injection was considered in [2–7] using Euler's equations. An analytic solution, based on the classic solution obtained by Hill for a spherical vortex, was derived in [2] for a sphere on the assumption of constant but different densities in the layers between the shock wave and the contact discontinuity and between the latter and the body. Certain results of a numerical solution of the problem of intensive injection at the surface of axisymmetric bodies of various forms, obtained by Godunov's method [3], are presented. Telenin's method was used in [4] for numerical investigation of flow around a sphere; the problem was solved in two formulations: in the first, flow parameters were determined for the whole of the shock layer, while in the second this was done for the sutface of contact discontinuity, which was not known prior to the solution of the problem, with the pressure specified by Newton's formula and flow parameters determined only in the layer of injected gases. The flow with injection over blunted cones was numerically investigated in [5] by the approximate method proposed by Maslen. The flow in the shock layer in the neighborhood of the stagnation line was considered in [6, 8], and intensive injection was investigated by methods of the boundary layer theory in [8–12].     

具有多参数的奇摄动非线性边值问题的摄动解

讨论含多个参数的高阶非线性方程的摄动解,在适当的条件下,先构造出外部解,再根据不同的边界层,利用伸展变量和幂级数展开式理论,构造问题的形式渐近解,最后利用微分不等式理论证明渐近解的一致有效性和渐近形态,把奇摄动非线性问题中的参数推广到多个参数.