ASYMPTOTIC ESTIMATION FOR SOLUTION OF A CLASS OF SEMI-LINEAR ROBIN PROBLEMS

A class of semi-linear Robin problem is considered. Under appropriate assumptions, the existence and asymptotic behavior of its solution are studied more carefully. Using stretched variables, the formal asymptotic expansion of solution for the problem is constructed and the uniform validity of the solution is obtained by using the method of upper and lower solution.

Asymptotic expansions of finite element solutions to Robin problems in H^3 and their application in extrapolation cascadic multigrid method

For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈H3.Based on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems effectively.Furthermore,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is obtained.Finally,some numerical experiments that confirm the theoretical analysis are presented.

Faber-Krahn Inequality for Robin Problems Involving p-Laplacian

The eigenvalue problem for the p-Laplace operator with Robin boundary conditions is considered in this paper. A Faber-Krahn type inequality is proved. More precisely, it is shown that amongst all the domains of fixed volume, the ball has the smallest first eigenvalue.

A CLASS OF NONLINEAR PREDATOR-PREY SINGULARLY PERTURBED ROBIN PROBLEMS FOR REACTION DIFFUSION SYSTEM

A class of nonlinear predator-prey singularly perturbed Robin problems for reaction diffusion systems are considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of solution for the initial boundary value problems are studied.

The Nonlinear Predator-Prey Singularly Perturbed Robin Initial Boundary Value Problems for Reaction Diffusion System

The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.

A Robin Problem for Quasi-linear System

In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using the theory of differential inequalities.

The spike layer solution to singular perturbation Robin boundary value problem for higher order elliptic equation

The singularly perturbed Robin boundary value problem for the higher order elliptic equation is considered.Under suitable conditions,the existence and asymptotic behavior of solution to the boundary value problems are studied.The uniform validity of its asymptotic expansion is proved by using the fixed point theorem.

Quasilinear Robin Problem with Boundary Perturbation

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.

DIAGONALIZATION METHOD FOR A SINGULARLY PERTURBED VECTOR ROBIN PROBLEM

In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic behavior of the solutions are obtained for a vector second-order nonlinear Robin problem of singular perturbation type.

Numerical Solutions to the Robin Inverse Problem with Nonnegativity Constraints

We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.

A Closed Form Solution to One Dimensional Robin Boundary Problems

Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species （e.g. enzymes）. In this paper, we will use reflected and absorbed Brownian motion and stochastic differential equations to construct a closed form solution to one dimensional Robin boundary problems. Meanwhile, we will give a reasonable explanation to the closed form solution from a stochastic point of view. Finally, we will extend the problem to Robin boundary problem with two boundary conditions and give a specific solution by resorting to a stopping time.

BOUNDARY AND CORNER LAYER BEHAVIOR IN SINGULARLY PERTURBED ROBIN BOUNDARY VALUE PROBLEM

This paper is concerned with boundary and corner layer behavior of the singularly perturbed Robin boundary value problem（RP） for the second-order nonlinear differential equations. The existence and asymptotic estimate of solutions of （RP） is discussed by appropriately constructing the bounding functions and using the theorv of differential inequality.

ASYMPTOTIC ESTIMatION OF ROBIN BOUNDARY VALUE PROBLEM FOR THIRD NONLINEAR EQUATION

In this paper, we study Robin boundary vlaue problem for third order equation εx'' = f(t, x, x', ω(ε)x', ε), x(0) = A, a1x'(0) - a2x'(0) = B, b1x'(1) +b2x'(1) = C. By means of upper and lower solutions method, and the existenceand asymptotic estimation of solution are established.

Robin Boundary Value Problem for One-Dimensional Landau–Lifshitz Equations

In this paper, we are concerned with the existence and uniqueness of global smooth solu- tion for the Robin boundary value problem of Landau Lifshitz equations in one dimension when the boundary value depends on time t. Yhrthermore, by viscosity vanishing approach, we get the existence and uniqueness of the problem without Gilbert damping term when the boundary value is independent of t.

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.

EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR NONLINEAR THIRD-ORDER ROBIN BOUNDARY VALUE PROBLEM WITH A TURNING POINT

The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear thirdorder Robin boundary value problem with a turning point. In order to achieve this aim, existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions. In this manner, the goal of this paper is gained by applying the existence and uniqueness results mentioned above.

MULTIPLE SOLUTIONS TO AN ASYMPTOTICALLY LINEAR ROBIN BOUNDARY VALUE PROBLEM

Under some weaker conditions,we prove the existence of at least two solutions to an asymptotically linear elliptic problem with Robin boundary value condition,using truncation arguments.Our results are also valid for the case of the so-called resonance at infinity.