Advances in Difference Equations (Oct 2021)

Reconstructing the right-hand side of the Rayleigh–Stokes problem with nonlocal in time condition

  • Phuong Nguyen Duc,
  • Ho Duy Binh,
  • Le Dinh Long,
  • Ho Thi Kim Van

DOI
https://doi.org/10.1186/s13662-021-03626-z
Journal volume & issue
Vol. 2021, no. 1
pp. 1 – 18

Abstract

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Abstract In this paper, the problem of finding the source function for the Rayleigh–Stokes equation is considered. According to Hadamard’s definition, the sought solution of this problem is both unstable and independent of continuous data. By using the fractional Tikhonov method, we give the regularized solutions and then deal with a priori error estimate between the exact solution and its regularized solutions. Finally, the proposed regularized methods have been verified by simple numerical experiments to check error estimate between the sought solution and the regularized solution.

Keywords