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A New Fourier Truncated Regularization Method for Semilinear Backward Parabolic Problems

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Abstract

We study the backward problem for non-linear (semilinear) parabolic partial differential equations in Hilbert spaces. The problem is severely ill-posed in the sense of Hadamard. Under a weak a priori assumption on the exact solution, we propose a new Fourier truncated regularization method for stabilising the ill-posed problem. In comparison with previous studies on solving the nonlinear backward problem, our method shows a significant improvement.

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Acknowledgement

The third author extends his appreciation to Distinguished Scientist Fellowship Program (DSFP) at King Saud University (Saudi Arabia).

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Authors and Affiliations

  1. Department of Mathematics, University of Science, Vietnam National University, Ho Chi Minh City, Viet Nam

    Tuan Nguyen Huy & Van Au Vo

  2. Laboratoire de Mathématiques Pôle Sciences et Technologie, Universié de La Rochelle, Aénue M. Crépeau, 17042, La Rochelle Cedex, France

    Mokhtar Kirane

  3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Mokhtar Kirane

  4. College of Science, Department of Mathematics, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    Bessem Samet

Authors
  1. Tuan Nguyen Huy
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  2. Mokhtar Kirane
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  3. Bessem Samet
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  4. Van Au Vo
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Correspondence to Mokhtar Kirane.

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Huy, T.N., Kirane, M., Samet, B. et al. A New Fourier Truncated Regularization Method for Semilinear Backward Parabolic Problems. Acta Appl Math 148, 143–155 (2017). https://doi.org/10.1007/s10440-016-0082-1

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  • DOI: https://doi.org/10.1007/s10440-016-0082-1

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