On reconstruction problems in inverse problems of determining unknown coefficients for non-linear partial differential equations

(1)给出了带摩擦项的二维驻波方程的出射本征函数及其散射振幅的存在性。我们还证明了在二维的摩擦系数是唯一重建的散射振幅在一个固定的低能量。(2)本文研究一维非线性波动方程确定场相关系数的边值反问题。我们证明了场相关系数的线性部分和二次部分是唯一地从边界测量重建的。

(1) We give the existence of outgoing eigen-function and its scattering amplitude for the two dimensional stationary wave equation with a friction term. We also prove in two dimensions that the friction coefficient is uniquely reconstructed from the scattering amplitude at a fixed low energy. (2) We study the inverse boundary value problem of determining a field-dependent coefficient for the non-linear wave equation in one space dimension. We prove that a linear part and a quadratic part of the field-dependent coefficient are uniquely reconstructed from the boundary measurements.