反应扩散方程中多个系数的恢复
Recovery of multiple coefficients in a reaction-diffusion equation
AI总结：
本文研究了从后期时间T处的解剖线值数据中恢复空间依赖的未知导率a(x)和势q(x)的逆问题，证明了唯一性和迭代方案的收敛性，并考虑了分数阶导数和非线性项耦合的更一般情况。
摘要：
本文考虑了从由后期时间T处的解剖线值构成的过定数据中恢复抛物方程中未知空间依赖导率a(x)和势q(x)的逆问题。我们证明了这两个系数的唯一性结果以及用于恢复这些系数的迭代方案的收敛性。我们还允许更一般的情况，特别是当通常的时间导数被分数阶导数代替，且势项与已知非线性项f的形式q(x)f(u)耦合时。
英文摘要：
This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity $a(x)$ and the potential $q(x)$ in a parabolic equation from overposed data consisting of the value of solution profiles taken at a later time $T$. We show both uniqueness results and the convergence of an iteration scheme designed to recover these coefficients. We also allow a more general setting, in particular when the usual time derivative is replaced by one of fractional order and when the potential term is coupled with a known nonlinearity $f$ of the form $q(x)f(u)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
