Approximation of an Inverse Initial Problem for a Biparabolic Equation

  • Huy Tuan NguyenEmail author
  • Mokhtar Kirane
  • Nam Danh Hua Quoc
  • Van Au Vo


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.


Backward problem Biparabolic equation Regularization method Error estimate 

Mathematics Subject Classification

35K99 47J06 47H10 35K05 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Huy Tuan Nguyen
    • 1
    Email author
  • Mokhtar Kirane
    • 2
    • 3
    • 4
  • Nam Danh Hua Quoc
    • 6
  • Van Au Vo
    • 5
  1. 1.Applied Analysis Research Group, Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi MinhVietnam
  2. 2.LaSIE, Facult des Sciences et TechnologiesUniversi de La RochelleLa Rochelle CedexFrance
  3. 3.NAAM Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  4. 4.RUDN UniversityMoscowRussia
  5. 5.Faculty of General SciencesCan Tho University of TechnologyCan ThoViet Nam
  6. 6.Department of Science ManagementThu Dau Mot UniversityThu Dau MotViet Nam

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