退化抛物型方程扩散系数识别的反问题

Inverse problem of diffusion coefficient identification for degenerate parabolic equations

研究通过附加条件来识别一维退化抛物型方程的扩散系数的反问题.主要讨论线性情况和幂指数型情况下的未知扩散系数的识别,运用了能量方法证明在一定时间内已知某个内部数据的情况下,识别常数系数和幂指数的唯一性和Lipschitz稳定性.

The inverse problem of identifying the diffusion coefficient of one-dimensional degenerate parabolic equation is studied by additional conditions.The identification of unknown diffusion coefficients in the linear case and the power exponential case is our major focus of discussion. The energy method is used to prove the uniqueness in the identification of the constant coefficient and the power exponent and Lipschitz stability when a certain internal data is known within a given time.