RECONSTRUCTION PROCEDURE FOR INVERSE PROBLEMS

获得了以下结果。(1)作为压电反问题研究的准备，证明了压电方程初边值问题的适定性。(2)证明了从Dirichlet到Neumann映射识别电导率方程中二次非线性项系数的唯一性。(3)与兰姆问题相关联的反问题的残余应力取决于深度的识别被认为是。对于一般情况给出了边界处的重建过程，对于特殊情况给出了内部的重建过程。(4)为了将衰减解应用于反问题，给出了具有解析电导率的各向异性导电方程边值问题的Cauchy数据与其解的奇异性之间的关系. (5)证明了含夹杂的Lame系统的解在夹杂直径趋于零时的渐近展开式。(6)给出了由远场方向图识别不可穿透障碍物及其物理特性的重建过程。(7)给出了从定域Dirichlet到Neumann映射逐点识别材料系数的重构公式。(8)证明了横观各向同性弹性方程和带残余应力的各向同性弹性方程的唯一延拓性。作为应用，证明了这些方程的Runge性质. (9)证明了带位势的Schrodinger方程的反边值问题在离散Dirichlet到Neumann映射下的近似识别。(10)证明了从Dirichlet到Neuman映射识别定常热传导方程对流项的反边值问题的全局唯一性。

The following results were obtained.(1) As a preparation of the research on the inverse problem for piezoelectricity, the well posedness of the initial boundary value problem for the equation of piezoelectricity was proven.(2) The uniqueness of identifying the coefficients of the nonlinear term of the second degree in the conductivety equation from the Dirichlet to Neumann map was proven.(3) The identification of the residual stress depending on the depth was considered for the inverse problem associated with the Lamb problem. The reconstruction procedure at the boundary was given for the general case and that of in the interior was given for a special case.(4) In order to apply the oscillating-decaying solution to inverse problem, the relation between the Cauchy data of the boundary value problem for anisotropic conductive equation with analytic conductivity and the singularity of its solution was shown.(5) The asymptotic expansion of the solution for the Lame system with inclusions as their diameter tends to zero was proven.(6) The reconstruction procedure of identifying impenetrable obstacles and their physical properties for acoustical inverse scattering problem from farfield pattern was given.(7) A reconstruction formula for identifying the material coefficients pointwisely from the localized Dirichlet to Neumann map was given.(8) The unique continuation for transversally isotropic elastic equation and isotropic elastic equation with residual stress were proven. Also, as their application Runge properties for these equations were proven.(9) An approximate identification for the inverse boundary value problem for the Schrodinger equation with potential from the discretized Dirichlet to Neumann map was proven.(10) The global uniqueness for the inverse boundary value problem for identifying the convection term of the steady state heat equation from the Dirichlet to Neuman map was proven.