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A New Fourier Truncated Regularization Method for Semilinear Backward Parabolic Problems

A New Fourier Truncated Regularization Method for Semilinear Backward Parabolic Problems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

A New Fourier Truncated Regularization Method for Semilinear Backward Parabolic Problems

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References (25)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer Science+Business Media Dordrecht
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-016-0082-1
Publisher site
See Article on Publisher Site

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.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Oct 31, 2016

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