一类非线性反向热传导问题的Fourier正则化方法

Fourier Truncation Regularization for a Class of Nonlinear Backward Heat Equation

考虑了非线性抛物方程反向热传导问题,这类问题是不适定的,即问题的解不连续依赖于测量数据.利用Fourier截断正则化方法恢复其不适定性,得到问题的一个正则近似解,并且给出正则解和精确解之间具有Hlder型的误差估计.

In this paper, we consider the nonlinear backward heat equation, which is severely ill-posed in the sense that the solution does not depend continuously on the data. A Fourier regularization method is proposed to solve this problem. For the regularization solution, the HSlder type stability estimate between the regularization solution and the exact solution is given.