Regularization of a multidimensional diffusion equation with conformable time derivative and discrete data

Donal O'Regan

doi:10.1002/mma.6133

Regularization of a multidimensional diffusion equation with conformable time derivative and discrete data

Donal O'Regan

Mathematics

Duy Tan University
University of Science Ho Chi Minh City
Ton Duc Thang University

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

19 Citations (Scopus)

Abstract

In this paper, we consider a backward problem for a nonlinear diffusion equation with a conformable derivative in the case of multidimensional and discrete data. We show that this problem is ill-posed and then we establish stable approximate solutions by two different regularization methods: the Fourier truncated method and the quasi-boundary value (QBV) method. Furthermore, the error between the approximate solution and the sought solution is given.

Original language	English (Ireland)
Pages (from-to)	2879-2891
Number of pages	13
Journal	Mathematical Methods In The Applied Sciences
Volume	44
Issue number	4
DOIs	https://doi.org/10.1002/mma.6133
Publication status	Published - 1 Dec 2019

Keywords

backward problem
conformable time derivative
diffusion equation
discrete data
regularization

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10.1002/mma.6133

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abstract = "In this paper, we consider a backward problem for a nonlinear diffusion equation with a conformable derivative in the case of multidimensional and discrete data. We show that this problem is ill-posed and then we establish stable approximate solutions by two different regularization methods: the Fourier truncated method and the quasi-boundary value (QBV) method. Furthermore, the error between the approximate solution and the sought solution is given.",

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AB - In this paper, we consider a backward problem for a nonlinear diffusion equation with a conformable derivative in the case of multidimensional and discrete data. We show that this problem is ill-posed and then we establish stable approximate solutions by two different regularization methods: the Fourier truncated method and the quasi-boundary value (QBV) method. Furthermore, the error between the approximate solution and the sought solution is given.

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KW - conformable time derivative

KW - diffusion equation

KW - discrete data

KW - regularization

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JF - Mathematical Methods In The Applied Sciences

IS - 4

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Regularization of a multidimensional diffusion equation with conformable time derivative and discrete data

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Keywords

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