Approximation of an Inverse Initial Problem for a Biparabolic Equation

Abstract

In this paper, we consider the problem of finding the initial distribution for the linear inhomogeneous and nonlinear biparabolic equation. The problem is severely ill-posed in the sense of Hadamard. First, we apply a general filter method to regularize the linear nonhomogeneous problem. Then, we also give a regularized solution and consider the convergence between the regularized solution and the sought solution. Under the a priori assumption on the exact solution belonging to a Gevrey space, we consider a generalized nonlinear problem by using the Fourier truncation method to obtain rigorous convergence estimates in the norms on Hilbert space and Hilbert scale space.

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Correspondence to Huy Tuan Nguyen.

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Nguyen, H.T., Kirane, M., Quoc, N.D.H. et al. Approximation of an Inverse Initial Problem for a Biparabolic Equation. Mediterr. J. Math. 15, 18 (2018). https://doi.org/10.1007/s00009-017-1053-0

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Mathematics Subject Classification

  • 35K99
  • 47J06
  • 47H10
  • 35K05

Keywords

  • Backward problem
  • Biparabolic equation
  • Regularization method
  • Error estimate