Determining the memory kernel from a fixed point measurement data for a parabolic equation with memory effect

作者：Wu, Bin; Wu, Siyuan; Yu, Jun^*; Wang, Zewen

来源：COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37(2): 1877-1893.

DOI：10.1007/s40314-017-0427-z

• Integro-differential equation
• Inverse problem
• Convolution kernel
• Memory effect
• Existence and uniqueness

We consider an inverse problem for a parabolic equation with memory effect. This inverse problem aims to identify the memory kernel function from a fixed point measurement data. Based on the fixed point arguments, we derive the global in time existence and uniqueness of our inverse problem. Moreover, we present a numerical algorithm to reconstruct the memory kernel function. Numerical simulations show the effectiveness of the proposed method.

• 出版日期2018-5
• 单位东华理工大学; 南京信息工程大学