标题： 用于流行病学系数逆问题的Carleman压缩映射方法 显示英文标题

标题： The Carleman Contraction Mapping Method for a Coefficient Inverse Problem of the Epidemiology

摘要： 通过求解三个耦合的非线性抛物方程组的系数逆问题来监测流行病的空间和时间传播。 为数值求解这个问题，开发了所谓卡勒曼压缩映射方法的一种版本。 在每次迭代中，通过加权拟逆方法求解一个带有不完整侧向柯西数据的线性问题，其中权重是卡勒曼权重函数。 这是在相应抛物算子的卡勒曼估计中作为权重使用的函数。 收敛分析确保了该过程的全局收敛性。 数值结果表明，该技术在噪声数据下表现出准确的性能。 显示英文摘要

摘要： It is proposed to monitor spatial and temporal spreads of epidemics via solution of a Coefficient Inverse Problem for a system of three coupled nonlinear parabolic equations. To solve this problem numerically, a version of the so-called Carleman contraction mapping method is developed for this problem. On each iteration, a linear problem with the incomplete lateral Cauchy data is solved by the weighted Quasi-Reversibility Method, where the weight is the Carleman Weight Function. This is the function, which is involved as the weight in the Carleman estimate for the corresponding parabolic operator. Convergence analysis ensures the global convergence of this procedure. Numerical results demonstrate an accurate performance of this technique for noisy data.