The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles

This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.

DynamicalSystem for Computing the Elliptic Boundary Problem

A dynamical system for computing the elliptic boundary problem is presented.It is shown that the proposed system is globally asymptotically stable.The system can be simulated by a neural network.Simulation results are valid and satisfactory.

Solvability of Elliptic Boundary Value Problems without Standard Landesman-Lazer Condition

In this paper we prove a very general result concerning solvability of the resonant problem: Δu+λku+g（x, u）=h（x）;u=0, xΩ, which immediately gives three generalized Landesman-Lazer conditions. The most interesting application of the general result is concerned with the problem when λk=λ1. in which case we prove solvability results for it under conditions which are not the standard Landesman-Lazer condition or only partly enjoy it. Furthermore, we propose a new sign condition and give a comprehensive extension of a main result of Figueiredo and Ni.

AN ITERATIVE PROCEDURE FOR DOMAIN DECOMPOSITION METHOD OF SECOND ORDER ELLIPTIC PROBLEM WITH MIXED BOUNDARY CONDITIONS

This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.

Transition-layer Solutions of Quasilinear Elliptic Boundary Blow-up Problems and Dirichlet Problems

We study profiles of positive solutions for quasilinear elliptic boundary blow-up problems and Dirichlet problems with the same equation：where ω 〉 0, a（x） is a continuous function satisfying 0 〈 a（x） 〈 1 for x ∈Ω, Ω is a bounded smooth domain in R^N. We will see that the profile of a minimal positive boundary blow-up solution of the equation shares some similarities to the profile of a positive minimizer solution of the equation with homogeneous Dirichlet boundary condition.

A NOTE ON THE NONCONFORMING FINITE ELEMENTS FOR ELLIPTIC PROBLEMS

In this paper, a class of rectangular finite elements for 2m-th-oder elliptic boundary value problems in n-dimension （m, n ≥1） is proposed in a canonical fashion, which includes the （2m - 1）-th Hermite interpolation element （n = 1）, the n-linear finite element （m = 1） and the Adini element （m = 2）. A nonconforming triangular finite element for the plate bending problem, with convergent order （O（h2）, is also proposed.

Multiple Solutions for a Fourth-order Asymptotically Linear Elliptic Problem

Under simple conditions, we prove the existence of three solutions for a fourth-order asymptotically linear elliptic boundary value problem. For the resonance case at infinity, we do not need to assume any more conditions to ensure the boundedness of the （PS） sequence of the corresponding functional.

EXISTENCE OF POSITIVE SOLUTION TO-Δu=f(x,u) WHEN f CHANGES SIGNS

The existence of positive solutions to the semlinear elliptic boundary value problem-Δ=f(x,u) in n and u= 0 on is studied in this paper. The result obtained differs from the other known results in that the positivity of the solution does not follow from the positivity of f.Our result roughly says that if Ω is not too wide in some one direction, there is always a positive solution even if fchanges signs, which is proved using the so-calles sub-super solution approach.

A Practical Algorithm for Determining the Optimal Pseudo-Boundary in the Method of Fundamental Solutions

One of the main difficulties in the application of the method of fundamental solutions(MFS)is the determination of the position of the pseudo-boundary on which are placed the singularities in terms of which the approximation is expressed.In this work,we propose a simple practical algorithm for determining an estimate of the pseudo-boundary which yields the most accurate MFS approximation when the method is applied to certain boundary value problems.Several numerical examples are provided.

LINEARIZATION OF A NONLINEAR PERIODIC BOUNDARY CONDITION RELATED TO CORROSION MODELING

We study galvanic currents on a heterogeneous surface. In electrochemistry, the oxidation-reduction reaction producing the current is commonly modeled by a nonlinear elliptic boundary value problem. The boundary condition is of exponential type with periodically varying parameters. We construct an approximation by first homogenizing the problem, and then linearizing about the homogenized solution. This approximation is far more accurate than both previous approximations or direct linearization. We establish convergence estimates for both the two and three-dimensional case and provide two-dimensional numerical experiments.

FINITE ELEMENT APPROXIMATION OF A NONLINEAR STEADY-STATE HEAT CONDUCTION PROBLEM

Examines a nonlinear partial differential equation of elliptic type with the homogeneous Dirichlet boundary conditions; Proof of the comparison and maximum principles; Approximation of the finite element; Introduction of a discrete analogue of the maximum principle for linear elements.

A CLASS OF NEW PARALLEL HYBRID ALGEBRAIC MULTILEVEL ITERATIONS

Presents preconditioning matrices having parallel computing function for the coefficient matrix and a class of parallel hybrid algebraic multilevel iteration methods for solving linear equations. Solution to elliptic boundary value problem; Discussion on symmetric positive definite matrix; Computational complexities.

Critical Point Theorems and Applications to Differential Equations

This paper contains a generalization of the well–known Palais–Smale andCerami compactness conditions. The compactness condition introduced is used to prove some generalexistence theorems for critical points. Some applications are given to differential equations.

SPLITTING A CONCAVE DOMAIN TO CONVEX SUBDOMAINS

We examine a steady-state heat radiation problem and its finite element approximation in Rd, d = 2, 3. A nonlinear Stefan-Boltzmann boundary condition is considered. Another nonlinearity is due to the fact that the temperature is always greater or equal than 0[K]. We prove two convergence theorems for piecewise linear finite element solutions.