The Singularly Perturbed Nonlinear Nonlocal Initial Boundary Value Problems for Reaction Diffusion Equations

The singularly perturbed nonlinear nonlocal initial boundary value problem for reaction diffusion equations is discussed. Under suitable conditions, the outer solution of the original problem is obtained. By using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. By using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied, and by educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are considered.     

具有边界摄动的非线性非局部反应扩散方程的奇摄动问题

A class of nonlinear nonlocal singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained; secondly, by using the stretched variable, the composing expansion method and the expanding theory of power series, the initial layer is constructed; and finally, by using the theory of differential inequalities the asymptotic behavior of solutions for initial boundary value problems is studied, and including some relational inequalities the existence and uniqueness of solutions for the original problem and the uniformly valid asymptotic estimation are discussed.     

A CLASS OF NONLINEAR NONLOCAL SINGULARLY PERTURBED PROBLEMS FOR ELLIPTIC EQUATION WITH BOUNDARY PERTURBATION

A class of nonlinear nonlocal singularly perturbed boundary value problems for elliptic equation with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series, the boundary layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems is studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed.     

A CLASS OF NONLINEAR SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH BOUNDARY PERTURBATION

A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptotic solution of the initial boundary value problems is studied.     

Shock wave solution for a class of nonlocal nonlinear singularly perturbed boundary value problems with turning point

The nonlocal nonlinear boundary value problem with turning point is considered. Leading the stretched variables the formal asymptotic solution of the original problem is constructed. And by using the theory of differential inequalities the existence and uniformly validity of solution for the original boundary value problems are proved. The contribution of this paper is that, the asymptotic behavior of solution is studied by using a simple and special method.     

A CLASS OF SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEM

The singularly perturbed boundary value problem for the nonlinear boundary conditions is considered. Under suitable conditions,the asymptotic behavior of solution for the original problems is studied by using theory of differential inequalities.     

ASYMPTOTIC BEHAVIOR OF SOLUTION FOR A CLASS OF REACTION DIFFUSION EQUATIONS

A class of initial boundary value problems for the reaction diffusion equations are considered. The asymptotic behavior of solution for the problem is obtained using the theory of differential inequality.     

GENERALIZED SOLUTION OF SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS

The singularly perturbed initial boundary value problem for reaction diffusion equation is considered. Under suitable conditions the existence, uniqueness and asymptotic behavior of the generalized solution for the problems are studied.     

具有边界摄动的拟线性Robin问题

A class of quasilinear Robin problems with boundary perturbation are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the boundary value problem is studied.     

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.     

一类具有边界摄动的非线性非局部反应扩散方程奇摄动问题

研究了一类具有边界摄动的非线性非局部反应扩散方程奇摄动Robin初始边值问题.在适当的条件下,首先求出了原问题的外部解,然后利用伸长变量、合成展开法和幂级数展开理论构造出解的初始层项,并由此得到解的形式渐近展开式.最后利用微分不等式理论,讨论了问题解的渐近性态并导出了几个有关的不等式,讨论了原问题解的存在唯一性和解的一致有效的渐近估计式.     

一类具有边界摄动的非线性泛函椭圆型方程奇摄动问题

研究了具有边界摄动的非线性泛函椭圆型方程奇摄动边值问题．在适当的条件下．利用伸长变量、微分不等式理论，讨论了问题解的渐近性态和原问题解的存在唯一性。     

一类非线性奇摄动系统的可解性及渐近解

研究了一类非线性微分系统的奇摄动边值问题.利用边界层校正法构造了形式渐近解和用微分不等式理论,证明了解的渐近展开式的一致有效性,得到了相应的定理,从而得到了原问题的可解性条件.     

Recovery of a Rapidly Oscillating Source in the Heat Equation from Solution Asymptotics

Four problems are solved in which a high-frequency source in the one-dimensional heat equation with homogeneous initial–boundary conditions is recovered from partial asymptotics of its solution. It is shown that the source can be completely recovered from an incomplete (two-term) asymptotic representation of the solution. The formulation of each source recovery problem is preceded by constructing and substantiating asymptotics of the solution to the original initial–boundary value problem.     

反应扩散方程解的渐近性态

研究了一类反应扩散方程初始边值问题. 利用微分不等式理论得到了问题解的渐近性态.