摘要
We consider the three dimensional Cauchy problem for the Laplace equation{uxx（x,y,z）＋uyy（x,y,z）＋uzz（x,y,z）=0,x∈R,y∈R,0〈z≤,u（x,y,0）=g（x,y）x∈R,y∈R,uz（x,y,0）=0,x∈R,y∈R,where the data is given at z = 0 and a solution is sought in the region x,y ∈ R,0 〈 z 〈 1. The problem is ill-posed, the solution （if it exists） doesn＇t depend continuously on the initial data. Using Galerkin method and Meyer wavelets, we get the uniform stable wavelet approximate solution. Furthermore, we shall give a recipe for choosing the coarse level resolution.
We consider the three dimensional Cauchy problem for the Laplace equation{uxx（x,y,z）＋uyy（x,y,z）＋uzz（x,y,z）=0,x∈R,y∈R,0〈z≤,u（x,y,0）=g（x,y）x∈R,y∈R,uz（x,y,0）=0,x∈R,y∈R,where the data is given at z = 0 and a solution is sought in the region x,y ∈ R,0 〈 z 〈 1. The problem is ill-posed, the solution （if it exists） doesn＇t depend continuously on the initial data. Using Galerkin method and Meyer wavelets, we get the uniform stable wavelet approximate solution. Furthermore, we shall give a recipe for choosing the coarse level resolution.
基金
Supported by Beijing Natural Science Foundation (No.1092003)
Beijing Educational Committee Foundation (No.00600054R1002)
