Abstract
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.
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Acknowledgements
The first author is supported by National Natural Science Foundation of China (11661004, 11601240). The fourth author is supported by National Natural Science Foundation of China (11561003), Ground Project of Science and Technology of Jiangxi Universities (KJLD14051).
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Communicated by Domingo Alberto Tarzia.
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Wu, B., Wu, S., Yu, J. et al. Determining the memory kernel from a fixed point measurement data for a parabolic equation with memory effect. Comp. Appl. Math. 37, 1877–1893 (2018). https://doi.org/10.1007/s40314-017-0427-z
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DOI: https://doi.org/10.1007/s40314-017-0427-z