A class of singularly perturbed initial boundary problem for reaction diffusion equation

The singularly perturbed initial boundary value problem for a class of reaction diffusion equation is considered. Under appropriate conditions, the existence-uniqueness and the asymptotic behavior of the solution are showed by using the fixed-point theorem.     

非线性奇摄动捕食-被捕食反应扩散系统

A class of nonlinear predator-prey reaction diffusion systems for singularly perturbedproblems are considered. Under suitable conditions, by using theory of differential inequalitiesthe existence and asymptotic behavior of solution for initial boundary value problems arestudied.     

The nonlinear singularly perturbed nonlocal reaction diffusion systems

In this paper the singularly perturbed initial boundary value problems for a nonlocal reaction diffusion system are considered. Using the iteration method and the comparison theorem, the existence and asymptotic behavior of solutions for the problem are studied.     

一类非线性奇摄动非局部反应扩散系统

Recently the nonlinear singularly perturbed problem has been investigated in theinternational academic circles[1 ,2 ] .Approximation methods have been developed andrefined,including the method of averaging,boundary layer method,matched asymptoticexpanision method and multiple scales method.Many scholars such as O' Malley,Jr.[3] ,Butuzov,Nefedov and Schneider[4] ,Kelley[5] ,Mizoguchi,Yanagida and Life[6] have done agreat deal of work.Using the method of differential inequality and other met…     

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.     

Asymptotic solution of nonlinear nonlocal singularly perturbed reaction diffusion problems with two parameters

A class of differential-difference reaction diffusion equations initial boundary problem with a small time delay is considered. Under suitable conditions and by using method of the stretched variable, the formal asymptotic solution is constructed. And then, by using the theory of differential inequalities the uniformly validity of solution is proved.     

三种群非线性食饵-捕食反应扩散系统奇摄动Robin问题

研究了一类非线性三种群食饵-捕食反应扩散系统奇摄动Robin问题.在适当的条件下,利用微分不等式理论,讨论了问题解的渐近性态.     

A class of singularly perturbed reaction diffusion integral differential system

Considertheinitialboundaryvalueproblemforthereactiondiffusionintegraldifferentialsystemoftheformeisapositiveparameter,x~(xl,x29...5x.)Cn,fidenotesaboundedregioninR",offsignifiesthesmoothboundaryoffiandkistheoutwardnormalderivativeonan,j:oofthenolilocaltermsTimisthelineintegralfromxotox.Theauthorhasdiscussedthisproblemundervarioussituationsusingthe.methodofdifferentialineqllalities['--8].Thispaperinvolvesaclassofinitialboundaryvalueproblemsforwidersingularlyperturbednonlinearreactiondiffusioni…     

Numerical method for a singularly perturbed convection-diffusion problem with delay

This paper deals with the singularly perturbed boundary value problem for a linear second-order delay differential equation. For the numerical solution of this problem, we use an exponentially fitted difference scheme on a uniform mesh which is accomplished by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form. It is shown that one gets first order convergence in the discrete maximum norm, independently of the perturbation parameter. Numerical results are presented which illustrate the theoretical results.     

A posteriori H1 error estimation for a singularly perturbed reaction diffusion problem on anisotropic meshes

The paper deals with a singularly perturbed reaction diffusionmodel problem. The focus is on reliable a posteriori error estimatorsfor the H¹ seminorm that can be applied to anisotropic finiteelement meshes. A residual error estimator and a local problemerror estimator are proposed and rigorously analysed. They arelocally equivalent, and both bound the error reliably. Threemodifications of these estimators are introduced and discussed. Much attention is given to the performance of the error estimatorin numerical experiments. This helps to identify those estimatorsthat are suitable for practical applications.