Final Value Problem for Parabolic Equation with Fractional Laplacian and Kirchhoff’s Term

Final Value Problem for Parabolic Equation with Fractional Laplacian and Kirchhoff’s Term

In this paper, we study a diffusion equation of the Kirchhoff type with a conformable fractional derivative. The global existence and uniqueness of mild solutions are established. Some regularity results for the mild solution are also derived. The main tools for analysis in this paper are the Banach...

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Main Authors: Nguyen Hoang Luc, Devendra Kumar, Le Dinh Long, Ho Thi Kim Van
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2021/7238678
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spelling doaj-9846f2769d624f0a9a591b666b5985b72021-07-12T02:12:06ZengHindawi LimitedJournal of Function Spaces2314-88882021-01-01202110.1155/2021/7238678Final Value Problem for Parabolic Equation with Fractional Laplacian and Kirchhoff’s TermNguyen Hoang Luc0Devendra Kumar1Le Dinh Long2Ho Thi Kim Van3Division of Applied MathematicsDepartment of MathematicsDivision of Applied MathematicsDivision of Applied MathematicsIn this paper, we study a diffusion equation of the Kirchhoff type with a conformable fractional derivative. The global existence and uniqueness of mild solutions are established. Some regularity results for the mild solution are also derived. The main tools for analysis in this paper are the Banach fixed point theory and Sobolev embeddings. In addition, to investigate the regularity, we also further study the nonwell-posed and give the regularized methods to get the correct approximate solution. With reasonable and appropriate input conditions, we can prove that the error between the regularized solution and the search solution is towards zero when δ tends to zero.http://dx.doi.org/10.1155/2021/7238678
collection DOAJ
language English
format Article
sources DOAJ
author Nguyen Hoang Luc
Devendra Kumar
Le Dinh Long
Ho Thi Kim Van
spellingShingle Nguyen Hoang Luc
Devendra Kumar
Le Dinh Long
Ho Thi Kim Van
Final Value Problem for Parabolic Equation with Fractional Laplacian and Kirchhoff’s Term
Journal of Function Spaces
author_facet Nguyen Hoang Luc
Devendra Kumar
Le Dinh Long
Ho Thi Kim Van
author_sort Nguyen Hoang Luc
title Final Value Problem for Parabolic Equation with Fractional Laplacian and Kirchhoff’s Term
title_short Final Value Problem for Parabolic Equation with Fractional Laplacian and Kirchhoff’s Term
title_full Final Value Problem for Parabolic Equation with Fractional Laplacian and Kirchhoff’s Term
title_fullStr Final Value Problem for Parabolic Equation with Fractional Laplacian and Kirchhoff’s Term
title_full_unstemmed Final Value Problem for Parabolic Equation with Fractional Laplacian and Kirchhoff’s Term
title_sort final value problem for parabolic equation with fractional laplacian and kirchhoff’s term
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8888
publishDate 2021-01-01
description In this paper, we study a diffusion equation of the Kirchhoff type with a conformable fractional derivative. The global existence and uniqueness of mild solutions are established. Some regularity results for the mild solution are also derived. The main tools for analysis in this paper are the Banach fixed point theory and Sobolev embeddings. In addition, to investigate the regularity, we also further study the nonwell-posed and give the regularized methods to get the correct approximate solution. With reasonable and appropriate input conditions, we can prove that the error between the regularized solution and the search solution is towards zero when δ tends to zero.
url http://dx.doi.org/10.1155/2021/7238678
work_keys_str_mv AT nguyenhoangluc finalvalueproblemforparabolicequationwithfractionallaplacianandkirchhoffsterm
AT devendrakumar finalvalueproblemforparabolicequationwithfractionallaplacianandkirchhoffsterm
AT ledinhlong finalvalueproblemforparabolicequationwithfractionallaplacianandkirchhoffsterm
AT hothikimvan finalvalueproblemforparabolicequationwithfractionallaplacianandkirchhoffsterm
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