Several Regularization Methods For A Backward Heat Equation With Robin Boundary Conditions

In many practical applications one wishes to reconstruct a temperature dis-tributions at 0≤t＜T from a measured temperature at a fixed time t = T＞0 in a heat conduction body. This problem is called the backward heat conduction problem. At present, there are few theoretical results in the literature for a back-ward heat conduction problem with Robin boundary conditions. In this paper, we will consider the following problem,This is a severely ill-posed problem. The small pertubation on h(x) can cause a large error on the solution, so the numerical implementation of this problem is very difficult. Since h(x) can only be measured, there must be measurement errors. Therefore providing some effective regularization methods for this problem are necessary. In this paper, we will deal with this problem by using some regu-larization methods including the modified Tikhonov method, the spectral cut-off method, the least squares method and the dual least squares method, and get the error estimates between the exact solution and corresponding regularized approx-imations. Numerical experiment shows that methods are effective.