Researches On The Numerical Inverse Problem For Parameter Identification Of The Conservative Variable Coefficient Anomalous Heat Conduction Model

The anomalous heat diffusion equation that described by fractional derivative model has many important applications in engineering,chemistry,materials,aerospace,mechanics,etc.In recent years,the theoretical analysis and numerical techniques of fractional heat conduction equations have been developed.However we may not be able to obtain the unknown components such as boundary values,thermal conductivity coefficients,initial conditions,or the strength of the heat source inside the medium in practice.We may estimate these physical quantities through specified observations,which lies in the scope of the inverse problem.This thesis is divided into four parts.Firstly,we give a brief introduction to our research background and literature reviews.Secondly,we display the theory of coefficient identification problem,the weak solution of the direct problem is founded in the form of M-L function.Next,we prove the uniqueness of the inverse problem of thermal conductivity identification and the estimation of fractional derivative order.In the third part,the finite difference method of the direct problem of the fractional heat conduction equation is proposed.Theoretical analyses is established to prove its unique solvability,stability,and convergence.Numerical examples are used to demonstrate the accuracy and convergence of the scheme.The fourth part mainly introduces the numerical algorithm of identifying space-dependent heat conduct coefficient,in which,the L-M algorithm is adopted.Numerical examples are used to verify the effectiveness of the parameter identification process.