Regularization Methods And Arithmetic Of The Unknown Source Identification Problem Of High Dimensional Heat Conduction Equation

Identifying the unknown source is a kind of the important problem for inverse problems. It has important application background in actual problems, such as exploring the new energy sources and looking for the sources of pollution. Because the haze is so serious in northern China today, it is particularly important to find out the sources of the haze. In this paper, we mainly use three regularization methods to deal with three ill-posed problems.In Chapter 2, we mainly consider to identify the unknown source depending only on space variable for one-dimensional heat equation with convection term. In the x axis, the diffusion of the medium and the heat conduction of the liquid can be expressed by the heat conduction equation with convection. We could obtain the regularized approximation by the mollification method with Guass kernel, and under the a priori and a posteriori parameter choice rules, we can all obtain the convergence error estimate.In Chapter 3 and Chapter 4, we mainly discuss the source identification problems of high dimensional heat equations in columnar domain and spherical domain.In this thesis, under the a posteriori parameter choice rules, we will use simplified Tikhonov and truncated regularization methods to obtain the regularized approximation and the Hlder type error estimate. Moreover we give a variety of numerical examples to verify the effectiveness of our methods.