A New Fourier Truncated Regularization Method for Semilinear Backward Parabolic Problems

Tuan Nguyen Huy; Mokhtar Kirane; Bessem Samet; Van Au Vo

doi:10.1007/s10440-016-0082-1

A New Fourier Truncated Regularization Method for Semilinear Backward Parabolic Problems

Tuan Nguyen Huy, Mokhtar Kirane, Bessem Samet, Van Au Vo

Mathematics

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11 Scopus citations

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.

Original language	British English
Pages (from-to)	143-155
Number of pages	13
Journal	Acta Applicandae Mathematicae
Volume	148
Issue number	1
DOIs	https://doi.org/10.1007/s10440-016-0082-1
State	Published - 1 Apr 2017

Keywords

Backward problem
Ill-posed problem
Nonlinear parabolic problem
Regularization method

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10.1007/s10440-016-0082-1

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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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AB - 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.

KW - Backward problem

KW - Ill-posed problem

KW - Nonlinear parabolic problem

KW - Regularization method

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A New Fourier Truncated Regularization Method for Semilinear Backward Parabolic Problems

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Keywords

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