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Regularization of a final value problem for a nonlinear biharmonic equation
Author(s) -
Hua Quoc Nam Danh,
Van Au Vo,
Huy Tuan Nguyen,
O'Regan Donal
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5771
Subject(s) - biharmonic equation , mathematics , hadamard transform , regularization (linguistics) , a priori and a posteriori , nonlinear system , well posed problem , mathematical analysis , backus–gilbert method , inverse problem , tikhonov regularization , boundary value problem , regularization perspectives on support vector machines , philosophy , physics , epistemology , quantum mechanics , artificial intelligence , computer science
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 ℒ 2 uniformly with respect to the space coordinate under some a priori assumptions on the solution.