On The Theory And Numerical Computation For The Boundary Problems Of The First Order Elliptic Systems

The dissertation discusses the Nonlinear Riemann boundary value problems and the Riemann-Hilbert boundary value problems for the first order elliptic systems , and discusses the Riemann-Hilbert boundary value problems for the generalized analytic function ( an especial form of the first order elliptic systems ) by means of the boundary element method .For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .The difficuty of the dissertation is the nonlinear of the equations or the boundary conditions . When proving the existence of the solution to the singular integral equation , we must estimate the norm of the operators , the process of the estimation is a complicated process .The boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function uses Cauchy integral formula as the foundation . The singularity of the Cauchy...