含双参数的三阶非线性两点边值问题的套层解(英文)

对含双参数且有套层解的一类三阶非线性微分方程的边值问题的渐近解做了估计 ,得到了任意次近似的一致有效的渐近展开式 .     

一类非线性奇摄动方程的匹配解法和解的精度估计

利用匹配渐近展开法,研究了一类非线性奇异摄动方程.在适当的条件下,得出了该类问题解的渐近展开式.并将结果应用于例子,对渐近解与精确解和用两变量方法求得的解进行比较,可知所得到的渐近解达到了较高精度.     

双参数非线性非局部奇摄动抛物型初始-边值问题的广义解

研究了一类广义抛物型方程奇摄动问题.首先在一定的条件下, 提出了一类具有两参数的非线性非局部广义抛物型方程初始 边值问题.其次证明了相应问题解的存在性.然后, 通过Fredholm积分方程得到了初始 边值问题的外部解.再利用泛函分析理论和伸长变量及多重尺度法, 分别构造了初始 边值问题广义解的边界层、初始层项,从而得到了问题的形式渐近展开式.最后利用不动点理论证明了对应的非线性非局部广义抛物型方程的奇异摄动初始 边值问题的广义解的渐近展开式的一致有效性.     

一类奇摄动边值问题解的套层现象

本文揭示了一类三阶半线性方程奇摄动边值问题解的“套层”现象。利用两次伸长变量的迭代，构造了解的形式渐近展开式。再用微分不等式理论，证明了该奇摄动问题渐近解的一致有效性。     

两参数非线性椭圆型方程的激波渐近解（英文）

本文讨论一类两参数非线性椭圆型方程边值问题.得到原问题的外部解,引入伸长变量和在边界和外部解的内部间断点附近设置局部坐标系,构造边界层和内部层校正项.在适当的条件下,利用微分不等式,证明边值问题激波解的存在性并研究解的渐近性态.     

一类具有瑞利摩擦水平正压的两层海洋风场系统[英文]

本文研究一类具有Rayleigh摩擦水平正压的两层海洋风场的非线性复杂系统.并在中纬度风场强迫的情况下,利用改进了的摄动方法,首先构造了退化系统的精确解;其次依次得到各次近似解;然后利用合成展开原理得到复杂系统的渐近解;最后,通过举例,说明得到的结果具有较好近似度的渐近解并讨论了对应解的物理意义.     

半线性方程ROBIN问题的角层解(英文)

本文讨论了一类半线性方程Robin边值问题.利用微分不等式理论,研究了边值问题角层解的存在性和渐近性态.     

非线性超抛物型方程广义渐近解的研究

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.     

一类半线性奇摄动问题解的渐近估计及应用

讨论了一类半线性奇摄动边值问题,构造了问题的具有代数型特点的左右边界层函数和内部角层函数,利用微分不等式理论证明了问题解的存在性,得到了解的渐近估计,给出了该类问题的一般性结论.并且将结论应用于一类燃烧问题的模型,得到了该模型的渐近估计.对有关文献的相关问题及其结果都作了相应的推广.     

二阶非线性奇摄动微分方程的渐近解

研究了二阶非线性奇摄动微分方程的边值问题.利用匹配原则和微分不等式原理,得到一阶非线性问题的渐近解,进而得到二阶奇摄动问题的解的渐近估计.     

THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR A CLASS OF STRONGLY NONLINEAR NON-AUTONOMOUS EQUATION

In this paper, using the singularly perturbed theory and the boundary layer corrective method, the asymptotic behavior of solution for a class of strongly nonlinear non-autonomous equations and the infection for asymptotic behavior of the solution with regard to the boundary condition are studied. According to the different regions of the boundary value, the asymptotic expansions of the solution for the original problem are obtained simply and conveniently.     

ASYMPTOTIC BEHAVIOR OF SINGULARLY PERTURBED SOLUTION FOR A CLASS OF ROBIN PROBLEM OF NONLINEAR NON-AUTONOMOUS EQUATION

In this paper, using the layer theory, a class of singularly perturbed Robin problem of nonlinear non-autonomous equation is considered. According to the different regions of the boundary value, the asymptotic behaviors of solution for the original problem are obtained simply and conveniently.     

非线性奇摄动抛物型方程初值问题的套层解

运用了初始层函数构造了一类非线性奇摄动抛物型方程初值问题解的渐近展开式,并证明了该展开式达到任意精度的一致有效性.     

THE INTERIOR LAYER SOLUTION TO NONLOCAL REACTION DIFFUSION EQUATIONS

An initial boundary value problem of semilinear nonlocal reaction diffusion equations is considered.Under some suitable conditions,using the asymptotic theory,the existence and asymptotic behavior of the interior layer solution to the initial boundary value problem are studied.     

具有超抛物型极限方程的非线性奇摄动反应扩散问题

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.     

Global Existence and Asymptotic Behavior of the Solution to 1-D Energy Transport Model for Semiconductors

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.     

THE CORNER LAYER SOLUTION TO ROBIN PROBLEM FOR REACTION DIFFUSION EQUATION

A class of Robin boundary value problem for reaction diffusion equation is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the corner layer solution to the initial boundary value problem are studied.     

A Free Boundary Problem Arising in Smoulder Combustion

The smouldering combustion is modeled as a free boundary problem here. By using the Duvaut's transform, the problem is reduced to a variational inequality. Existence and uniqueness are established. Tbe properties of the free boundary are studied in various cases. The asymptotic behavior of the free boundary with respect to the parameter is rigorously proved, which confirms the result of a previous work by J. Adler and D. M. Herbert, obtained by using asymptotic expansion. Furthermore, we show that the time dependent problem will actually converge to a travelling wave solution if the boundary data converge to the corresponding travelling wave solution.     

A CLASS OF STRONGLY NONLINEAR SINGULARLY PERTURBED INTERIOR LAYER PROBLEMS

In this paper, a class of strongly nonlinear singularly perturbed interior layer problems are considered by the theory of differential inequalities and the corrective theory of interior layer. The existence of solution is proved and the asymptotic behavior of solution for the boundary value problems are studied. And the satisfying result is obtained.