Inversion Of Source Term And Initial Distribution Of Heat Conduction Equation And Its Algorithm

The inverse time problem and source term inversion of heat conduction equation with serious ill-posed are always one of the research hot spots.They are widely used in rivers,lakes,atmosphere and other practical science and engineering.In this dissertation,we mainly consider two kinds of ill-posed problems in the inversion of heat conduction equation,that is,the inversion of source term of heat conduction equation,the simultaneous inversion of source term and initial distribution.The first chapter introduces the research significance of heat conduction equation inversion,the source term inversion of heat conduction equation,the present research situation of simultaneous inversion of source term and initial distribution,as well as the main research contents and innovation points of this dissertation.The second chapter introduces some important inequalities,general regularization theory and Tikhonov regularization method.In the third chapter,the source term inversion of heat conduction equation in bounded domain is studied.Firstly,the conditional stability of source term inversion is analyzed,and an exponential regularization method is constructed to reconstruct source term.Then,the convergence and error estimation of regularization solution of exponential regularization method under prior selection regularization parameter and posterior selection regularization parameter are given.Finally,the effectiveness of the algorithm is verified by numerical simulation results.In chapter 4,the simultaneous inversion of source term and initial distribution of heat conduction equations in bounded domain is studied.Firstly,the conditional stability of source term and initial distribution inversion is analyzed,and a two-stage exponential regularization method for reconstructing source term and initial distribution of heat conduction equation is constructed.The convergence and error estimation of regularization solution of exponential regularization method under prior selection regularization parameter and posterior selection regularization parameter are given.Then,an exponential regularization method which can calculate the source term and initial distribution simultaneously is presented.Finally,the effectiveness of the two algorithms is verified by numerical simulation results.The fifth chapter summarizes the content of the distribution and prospects the future work.