Regularization Methods For Three Inverse Heat Conduction Problems

Inverse heat conduction problem is one of the central issue of the inverse problems in mathematical physics,which has important practical application background.The research on inverse heat conduction is mainly the regularization method under a prior condition,and the research results of a posteriori regularization method are relatively few.This thesis applies the a-prior and a-posterior regularization methods for a one-dimensional inverse heat conduction problem(IHCP),a one-dimensional IHCP with convection term and a two-dimensional IHCP.This thesis includes the following three parts.In chapter 2,we consider the one-dimensional IHCP in the bounded time domain.By using the H(?)lder inequality,we can obtain the conditional stability of the problem.Using the spectral truncation regularization method,and construct the regularized approximate solution of the ill-posed problem.Under a-prior and a-posterior regularization parameter selection rules,we derive H(?)lder error estimates between the regularized approximate solution and exact solution.In chapter 3,one-dimensional IHCP with convective terms is studied.For this ill-posed problem,the Fourier technology is used to find the formal solution and the conditional stability of the problem is given.We use an iterative regularization method for studying the problem and obtain regularized approximate solution for it.We give two error estimates with a-prior and a-posterior regularization parameter choice rules.In chapter 4,we talk about the two-dimensional IHCP.Using Fourier technology first,to find the formal solution and the stability of the ill-posed problem is given.Then the modified inverse boundary regularization method is used for the problem and obtain regularized solution for it.Two error estimates are obtained under a-prior and a-posterior regularization approximate parameter choice rules.