Periodic solution to a kind of singularly perturbed differential equations of parabolic type in chemical kinetics

This paper deals with the problem on the periodic solution for the singularly perturbeddifferential equations of parabolic type originating from chemical kinetics in stratifiedmedia,A uniformly valid asymptotic solution is constructed and the related asymptoticestimate is given.     

A class of singularly perturbed reaction diffusion systems

A class of singularly perturbed reaction diffusion systems are considered. Under suitable conditions, using the comparison theorem the asymptotic behavior of solution for the initial boundary value problems is studied. Project supported by the National Natural Science Foundation of China     

The numerical solution of a singularly perturbed problem for quasilinear parabolic differential equation

We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform convergence in the sense of discrete L~2 norm is proved and numerical examples are presented.     

The nonlinear nonlocal singularly perturbed problems for reaction diffusion equations

A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations 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 initial layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed. Foundation items: the National Natural Science Foundation of China (10071048); the “Hunfred Talents Project” by Chinese Academy of Sciences Biography: Mo Jia-qi (1937−)     

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

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

SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMI-LINEAR RETARDED DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

IntroductionInthispaper,westudiedakindofboundaryvalueproblems (BVPs)forsemi_linearretardeddifferentialequationwithnonlinearboundarycondition :　　　　εx″(t) =f(t,x(t) ,x(t-ε) ,ε) ,　　t∈(0 ,1 ) ,(1 )　　　　x(t) =φ(t,ε) ,　t∈[-ε0 ,0 ] ,h(x(1 ) ,x′(1 ) ,ε) =A(ε) ,(2 )whereε>0isasmallparameterandε0 isasufficientlysmallpositiveconstant.ThereweremanyresultsofstudyingonsingularlyperturbedboundaryvalueproblemforretardeddifferentialequationinRefs.[1～5] .Butthosestudiespossessedanesse…     

Contrast structure for singular singularly perturbed boundary value problem

The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the step- type solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.     

Singular perturbation of initial-boundary value problems for a class of reaction diffusion systems

In this paper,a class of singularly perturbed initial-boundary value problems for thereaction diffusion systems is considered.Using the theory of differential inequality,weprove that the initial-boundary value problems have a solution and obtain their asymptoticexpansion.     

Numerical solutions for singularly perturbed semi-linear parabolic equation

In this paper,we discuss singularly perturbed semi-linear parabolic equations for one dimension and two dimension,we find numerical solutions by using both the line-method and the exact difference scheme on a special non-uniform discretization mesh.The uniform convergence in e of the first order accuracy is obtained.     

THE NUMERICAL SOLUTION OF A SINGULARLY PERTURBED PROBLEM FOR SEMILINEAR PARABOLIC DIFFERENTIAL EQUATION

The numerical solution of a singularly perturbed problem for the semilinear parabolicdifferential equation with parabolic boundary layers is discussed.A nonlinear two-leveldifference scheme is constructed on the special non-uniform grids.The uniform convergenceof this scheme is proved and some numerical examples are given.     

An exponentially fitted difference scheme for the hyperbolic-hyperbolic singularly perturbed initial-boundary value problem

In this paper we discuss,an initial-boundary value problem of hyperbolic type with firstderivative with respect to x.The asymptotic solution is constructed and its uniform validityis proved under weader compatibility conditions.Then we develop an exponentially fitteddifference scheme and establish discrete energy inequality.Finally,we prove that thesolution of difference problem uniformly converges to the solution of the original problem.     

Boundary value problem for a singularly perturbed nonlinear system

I.Intr0ducti0n'Manyresultshavebeeng0tinstudyingthesingu1arperturbation0fboundaryvalueproblemfornonlinearsystemeg#=j(t,g,y',8)(l.l)bythemethodandthetechniqueofdiagonalizationl'~'l.Thepapersarebasedonsucha.conditionthattheeigenvaluesofJacobimatrixlu'offwit…     

Numerical solution of a singularly perturbed elliptichyperbolic partial differential equation on a nonuniform discretization mesh

In this paper, we consider the upwind difference scheme for singular perturbation problem (1.1). On a special discretization mesh, it is proved that the solution of the upwind difference scheme is first order convergent, uniformly in the small parameter ε, to the solution of problem (1.1). Numerical results are finally provided.     

A uniformly convergent finite difference method for a singularly perturbed initial value problem

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｕｒｐｏｓｅｏｆｔｈｉｓｐａｐｅｒｉｓｔｏｄｅｖｅｌｏｐａｃｕｒａｔｅｄｉｆｅｒｅｎｃｅｍｅｔｈｏｄｆｏｒｔｈｅｆｏｌｏｗｉｎｇｉｎｉｔｉａｌｖａｌｕｅｐｒｏｂｌｅｍ,ｗｈｉｃｈｉｓｉｎｓｉｎｇｕｌａｒｐｅｒｔｕｒｂａ...     

Boundary and interior layer behavior for singularly perturbed vector problem

In this paper,we consider the vector nonlinear boundary value problem:εy~v=f(x,y,z,y′,ε),y(0)=A_1,y(1)=B_1εz~v=g(x,y,z,z′,ε),z(0)=A_2,z(1)=B_2whereε>0 is a small parameter,0≤x≤1 ,f and g are continuous functions in R~4,Under appropriate assumptions,by means of the differential inequalities,we demonstratethe existence and estimation,involving boundary and interior layers,of the solutions to theabove problem.     

Asymptotic solution of a singularly perturbed nonlinear state regulator problem

I.1utroductlouWeconsidcrthenonlinearstateregulatorproblemsconsistingofthesystemontheinterval0't相似文献   

NUMERICAL SOLUTION OF THE SINGULARLY PERTURBED PROBLEM WITH NONLOCAL BOUNDARY CONDITION

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｉｓｐａｐｅｒｉｓｃｏｎｃｅｒｎｅｄｗｉｔｈｔｈｅｎｕｍｅｒｉｃａｌｓｏｌｕｔｉｏｎ ,ｂｙｆｉｎｉｔｅｄｉｆｆｅｒｅｎｃｅｍｅｔｈｏｄ ,ｏｆｔｈｅｆｏｌｌｏｗｉｎｇｓｉｎｇｕｌａｒｌｙｐｅｒｔｕｒｂｅｄｎｏｎｌｏｃａｌｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍ :Ｌｕ≡-εｕ″ +ａ(ｘ)ｕ=ｆ(ｘ)　　 ( 0 <ｘ<ｌ) ,( 1 )Ｌ0 ｕ≡-εｕ′( 0 ) +γｕ( 0 ) =μ0 , ( 2 )Ｌ1ｕ≡ｕ(ｌ) -δｕ(ｄ) =μｌ　　 ( 0 <ｄ<ｌ) ,( 3 )ｗｈｅｒｅεｉｓａｓｍａｌｌｐｏｓｉｔｉｖｅｐａｒａｍｅｔｅｒ,…     

Transition layers for singularly perturbed delay differential equations with monotone nonlinearities

Transition layers arising from square-wave-like periodic solutions of a singularly perturbed delay differential equation are studied. Such transition layers correspond to heteroclinic orbits connecting a pair of equilibria of an associated system of transition layer equations. Assuming a monotonicity condition in the nonlinearity, we prove these transition layer equations possess a unique heteroclinic orbit, and that this orbit is monotone. The proof involves a global continuation for heteroclinic orbits.     

Initial layer phenomena for a class of singular perturbed nonlinear system with slow variables

The initial layer phenomena for a class of singular perturbed nonlinear system with slow variables are studied. By introducing stretchy variables with different quantity levels and constructing the correction term of initial layer with different “ thickness“, the Norder approximate expansion of perturbed solution concerning small parameter is obtained, and the “ multiple layer“ phenomena of perturbed solutions are revealed. Using the fixed point theorem, the existence of perturbed solution is proved, and the uniformly valid asymptotic expansion of the solutions is given as well.     

Singularly perturbed solution for weakly nonlinear equations with two parameters

A class of singularly perturbed boundary value problems of weakly non- linear equation for fourth order on the interval[a,b]with two parameters is considered. Under suitable conditions,firstly,the reduced solution and formal outer solution are con- structed using the expansion method of power series.Secondly,using the transformation of stretched variable,the first boundary layer corrective term near x=a is constructed which possesses exponential attenuation behavior.Then,using the stronger transfor- mation of stretched variable,the second boundary layer corrective term near x=a is constructed,which also possesses exponential attenuation behavior.The thickness of second boundary layer is smaller than the first one and forms a cover layer near x=a. Finally,using the theory of differential inequalities,the existence,uniform validity in the whole interval[a,b]and asymptotic behavior of solution for the original boundary value problem are proved.Satisfying results are obtained.