具非线性边值条件的二维Helmholtz方程的边界元分析

Boundary Element Analysis of Two─dimensions Helmholtz Equation with Nonlinear Boundary Value Condition

本文将具有非线性边值条件的二维Ｈｅｌｍｈｏｌｔｚ方程化为等价的非线性拟微分算子方程。除了说明该方程解的存在唯一性外，还利用Ｇａｌｅｒｋｉｎ方法得到了非线性离散方程组、根据不动点指数定理证明了非线性方程组的存在唯一性，根据ａ－正常理论给出了相关的正则性定理。文末采用线性化技巧，给出了拟最优化估计。

in this paper, we reformulate the two-dimensional Helmholtz equation with nonlinear boundary value condition as an equivalent nonlinear quasi-differential operator equation as an equivalent nonlinear quasi-differential operator equation. In addition to the indication of existence and uniqueness of the solution of this equation, we have got the discretized system of equations by Galerkin's method. According to the fixed point index theorm, we have proved the existence and uniqueness of the solution of nonlinear system of equations. By use of a-proper theory, we have got the relevant regular theorm. Finally, using the Linearized technology, we have obtained the quasi-optimal estimation.