A New Fourier Truncated Regularization Method for Semilinear Backward Parabolic Problems |
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| Authors: | Tuan Nguyen Huy Mokhtar Kirane Bessem Samet Van Au Vo |
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| Institution: | 1.Department of Mathematics, University of Science,Vietnam National University,Ho Chi Minh City,Viet Nam;2.Laboratoire de Mathématiques P?le Sciences et Technologie,Universié de La Rochelle,La Rochelle Cedex,France;3.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science,King Abdulaziz University,Jeddah,Saudi Arabia;4.College of Science, Department of Mathematics,King Saud University,Riyadh,Saudi Arabia |
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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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