论文标题
带有最终数据的抛物线方程中的系数识别
Coefficient identification in parabolic equations with final data
论文作者
论文摘要
在这项工作中，我们从单个最终数据的知识中确定了抛物线方程中的二阶系数。在相关椭圆操作员和初始状态的特征值浓度的假设下，我们显示了溶液的独特性，当最终时间足够大时，我们得出了lipschitz稳定性估计值。 Lipschitz稳定性常数相对于最后一次，这使反转不足。稳定性估计的证明是基于根据相关椭圆运算符的本征函数将溶液对抛物线方程的光谱分解，以及求解非线性固定传输方程本身的临时方法。
In this work we determine the second-order coefficient in a parabolic equation from the knowledge of a single final data. Under assumptions on the concentration of eigenvalues of the associated elliptic operator, and the initial state, we show the uniqueness of solution, and we derive a Lipschitz stability estimate for the inversion when the final time is large enough. The Lipschitz stability constant grows exponentially with respect to the final time, which makes the inversion ill-posed. The proof of the stability estimate is based on a spectral decomposition of the solution to the parabolic equation in terms of the eigenfunctions of the associated elliptic operator, and an ad hoc method to solve a nonlinear stationary transport equation that is itself of interest.
