Regularized solution for a biharmonic equation with discrete data

Authors: Trần Ngọc Thạch, Donal O'Regan, Nguyễn Huy Tuấn, Nguyễn Huy Tuấn, Donal O’Regan,

https://doi.org/10.3934/eect.2020008

Publisher, magazine: ,

Publication year: 2020

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Abstract

In this work, we focus on the Cauchy problem for the biharmonic equation associated with random data. In general, the problem is severely ill-posed in the sense of Hadamard, i.e, the solution does not depend continuously on the data. To regularize the instable solution of the problem, we apply a nonparametric regression associated with the Fourier truncation method. Also we will present a convergence result.

Tags: Ill-posed problem, regularized method, estimate, biharmonic equation, Cauchy problem, discrete data.