Regularization of a final value problem for a nonlinear biharmonic equation

Danh Hua Quoc Nam; Vo Van Au; Nguyen Huy Tuan; Donal O'Regan

doi:10.1002/mma.5771

Regularization of a final value problem for a nonlinear biharmonic equation

Danh Hua Quoc Nam, Vo Van Au, Nguyen Huy Tuan, Donal O'Regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper, we consider the nonlinear biharmonic equation. The problem is ill-posed in the sense of Hadamard. To obtain a stable numerical solution, we consider a regularization method. We show rigourously, with error estimates provided, that the corresponding regularized solutions converge to the true solution strongly in (Formula presented.) uniformly with respect to the space coordinate under some a priori assumptions on the solution.

Original language	English
Pages (from-to)	6672-6685
Number of pages	14
Journal	Mathematical Methods in the Applied Sciences
Volume	42
Issue number	18
DOIs	https://doi.org/10.1002/mma.5771
Publication status	Published - 1 Dec 2019

Keywords

backward problem
biharmonic equation
error estimate
polyharmonic problem
regularization method

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10.1002/mma.5771

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abstract = "In this paper, we consider the nonlinear biharmonic equation. The problem is ill-posed in the sense of Hadamard. To obtain a stable numerical solution, we consider a regularization method. We show rigourously, with error estimates provided, that the corresponding regularized solutions converge to the true solution strongly in (Formula presented.) uniformly with respect to the space coordinate under some a priori assumptions on the solution.",

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AU - Van Au, Vo

AU - Huy Tuan, Nguyen

AU - O'Regan, Donal

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KW - backward problem

KW - biharmonic equation

KW - error estimate

KW - polyharmonic problem

KW - regularization method

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ER -

Regularization of a final value problem for a nonlinear biharmonic equation

Abstract

Keywords

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