Regularization of a final value problem for a nonlinear biharmonic equation

Authors: Nguyễn Huy Tuấn, Võ Văn Âu, Donal O'Regan, Danh Hứa Quốc Nam, Nguyễn Huy Tuấn, Donal O’Regan,

https://doi.org/10.1002/mma.5771

Publisher, magazine: ,

Publication year: 2019

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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 urn:x-wiley:mma:media:mma5771:mma5771-math-0001 uniformly with respect to the space coordinate under some a priori assumptions on the solution.

Tags: backward problem, biharmonic equation, error estimate, polyharmonic problem, regularization method