一个抛物型方程不适定问题的小波正则化方法  

Wavelet Regularization for an Ill-Posed Problem of Parabolic Equation

作　　者：邱春雨[1] 傅初黎[1] 

机构地区：[1]兰州大学数学系,兰州730000

出　　处：《数学物理学报（A辑）》2002年第3期361-372,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金 (批准号 49875 0 2 4)

摘　　要：一维抛物型方程如下定解问题ut+ ux =uxx,0≤ x <∞ ,0≤ t<∞ ,u( 1 ,t) =g( t) ,0≤ t<∞ ,u( x,0 ) =0 ,x≥ 0 .是一个不适定问题 .数据 g的微小变化可以引起解的巨大误差 .该文通过构造一个在频域具紧支集的小波并在尺度空间上展开数据和解 ,滤除了高频分量 ,并结和 Galerkin方法 ,建立了一种逼近准确解的正则化方法 ,恢复了解对数据的连续依赖性 。The sideways parabolic equation in the quarter plane\$\$[HL(2:1,Z;2,Z]u\-t+u\-x=u\-\{xx\}, 0≤x<∞,0≤t<∞, u(1,t)=g(t), 0≤t<∞, u(x,0)=0, x≥0is considered. This is a severely ill posed problem: a small peturbation in the data \$g\$, may cause dramatically large errors in the solution. A wavelet whose Fourier transform has compact support is constructed, and by expanding the data and the solution in a basis of this wavelets, high frequency componets can be filtered away. The continuous dependence on the data is restored by using a wavelet Galerkin approach. The error estimate is also given.

关 键 词：抛物型方程 不适定问题 小波 正则化方法 反问题 

分 类 号：O175.26[理学—数学]