Inverse Time Problem Of Two-dimensional Degraded Parabolic Equation

Degenerate parabolic equations have important applications in many practical engineering fields,such as material engineering,transportation and financial engineering.The inverse problem of two kinds of inverse heat conduction problems are discussed.Through relevant theoretical analysis,the second kind of degenerate parabolic equation is numerically simulated by landweber iterative method and CGM iterative method,and the numerical results show the feasibility and effectiveness of the proposed method.This paper is mainly divided into the following five chapters:The first chapter is the introduction part,mainly describes the research status at home and abroad related to this paper and the main work of this paper.In chapter two,we mainly consider the Robin coefficient inversion problem of a kind of heat conduction equations with variable coefficients.The Robin coefficient is only related to time.Here the first variational formula is given,the uniqueness is proved by using the variational formula,second time discrete model is given,based on linear variational form of discretization,a series of a prior estimate are derived,the existence of weak solutions is proved,and it's error is analyzed.In chapter three,we study the inverse problem of the initial value of a two-dimensional degenerate parabolic equation,which thermal conductivity varies with the spatial variable.Firstly,the finite volume method is used to construct the difference scheme of the positive problem.Secondly,the stability and convergence of the difference equations are discussed.In chapter four,mainly discusses the initial value inverse problem of reconstructing two-dimensional degenerate parabolic equation using terminal observations problem from the point of view numerical analysis.To solve the problem in Landweber iteration and CGM iteration methods,a numerical example and corresponding numerical results are given.Then a numerical example and corresponding numerical results are given.The numerical results show that algorithms are stable and the convergence speed is faster.In chapter five summarizes the conclusions and shortcomings of this paper,discusses the follow-up work of this paper,and makes a further prospect for the future work.