Regularized solution for a biharmonic equation with discrete data

Tran Ngoc Thach; Nguyen Huy Tuan; Donal O’regan

doi:10.3934/eect.2020008

Regularized solution for a biharmonic equation with discrete data

Tran Ngoc Thach
, Nguyen Huy Tuan
, Donal O’regan

Mathematics

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

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	341-358
Number of pages	18
Journal	Evolution Equations and Control Theory
Volume	9
Issue number	2
DOIs	https://doi.org/10.3934/eect.2020008
Publication status	Published - 1 Jun 2020

Keywords

And phrases
Biharmonic equation
Cauchy problem
Discrete data
Estimate
Ill-posed problem
Regularized method

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Thach, TN;Tuan, NH;O'Regan, D

Access to Document

10.3934/eect.2020008

Cite this

@article{60dc8a8d184a487893afc956c1a428ca,

title = "Regularized solution for a biharmonic equation with discrete data",

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.",

keywords = "And phrases, Biharmonic equation, Cauchy problem, Discrete data, Estimate, Ill-posed problem, Regularized method",

author = "Thach, \{Tran Ngoc\} and Tuan, \{Nguyen Huy\} and Donal O{\textquoteright}regan",

year = "2020",

month = jun,

day = "1",

doi = "10.3934/eect.2020008",

language = "English",

volume = "9",

pages = "341--358",

journal = "Evolution Equations and Control Theory",

issn = "2163-2472",

publisher = "American Institute of Mathematical Sciences",

number = "2",

}

TY - JOUR

T1 - Regularized solution for a biharmonic equation with discrete data

AU - Thach, Tran Ngoc

AU - Tuan, Nguyen Huy

AU - O’regan, Donal

PY - 2020/6/1

Y1 - 2020/6/1

N2 - 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.

AB - 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.

KW - And phrases

KW - Biharmonic equation

KW - Cauchy problem

KW - Discrete data

KW - Estimate

KW - Ill-posed problem

KW - Regularized method

UR - https://www.scopus.com/pages/publications/85083287461

U2 - 10.3934/eect.2020008

DO - 10.3934/eect.2020008

M3 - Article

SN - 2163-2472

VL - 9

SP - 341

EP - 358

JO - Evolution Equations and Control Theory

JF - Evolution Equations and Control Theory

IS - 2

ER -

Regularized solution for a biharmonic equation with discrete data

Abstract

Keywords

Authors (Note for portal: view the doc link for the full list of authors)

Access to Document

Other files and links

Fingerprint

Cite this