On a final value problem for a nonhomogeneous fractional pseudo-parabolic equation
In this paper, we are interested in finding the function u(t,x),(t,x)∈[0,T)×Ω from the final data u(T,x)=ϕ(x), satisfies a nonhomogeneous fractional pseudo-parabolic equation. The problem is stable for the cases σ<ν in the sense that the solution of the problem is regularity-loss and we discuss t...
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doaj-ba840cd401464a2cbe878a52babdf9412021-06-02T14:25:31ZengElsevierAlexandria Engineering Journal1110-01682020-12-0159643534364On a final value problem for a nonhomogeneous fractional pseudo-parabolic equationNguyen Hoang Luc0Devendra Kumar1Le Thi Diem Hang2Nguyen Huu Can3Institute of Research and Development, Duy Tan University, Da Nang 550000, Viet NamDepartment of Mathematics, University of Rajasthan, Jaipur, IndiaDepartment of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Viet Nam; Vietnam National University, Ho Chi Minh City, Viet Nam; Department of Mathematical Economics, Banking University of Ho Chi Minh City, Ho Chi Minh City, VietnamApplied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam; Corresponding author.In this paper, we are interested in finding the function u(t,x),(t,x)∈[0,T)×Ω from the final data u(T,x)=ϕ(x), satisfies a nonhomogeneous fractional pseudo-parabolic equation. The problem is stable for the cases σ<ν in the sense that the solution of the problem is regularity-loss and we discuss the regularity of the solution to this problem. For the case σ>ν, the problem is ill-posed (in the sense of Hadamard). We propose the general filtering method to regularize this problem. The well-posedness of the regularized problem and some regularity estimates of the regularized solution are obtained. Moreover, error estimates are established under some a priori conditions of the sought solution. The numerical illustrations are given to show the convergence of our method.http://www.sciencedirect.com/science/article/pii/S111001682030365335K5535K7035K9247A5247J06 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Nguyen Hoang Luc Devendra Kumar Le Thi Diem Hang Nguyen Huu Can |
spellingShingle |
Nguyen Hoang Luc Devendra Kumar Le Thi Diem Hang Nguyen Huu Can On a final value problem for a nonhomogeneous fractional pseudo-parabolic equation Alexandria Engineering Journal 35K55 35K70 35K92 47A52 47J06 |
author_facet |
Nguyen Hoang Luc Devendra Kumar Le Thi Diem Hang Nguyen Huu Can |
author_sort |
Nguyen Hoang Luc |
title |
On a final value problem for a nonhomogeneous fractional pseudo-parabolic equation |
title_short |
On a final value problem for a nonhomogeneous fractional pseudo-parabolic equation |
title_full |
On a final value problem for a nonhomogeneous fractional pseudo-parabolic equation |
title_fullStr |
On a final value problem for a nonhomogeneous fractional pseudo-parabolic equation |
title_full_unstemmed |
On a final value problem for a nonhomogeneous fractional pseudo-parabolic equation |
title_sort |
on a final value problem for a nonhomogeneous fractional pseudo-parabolic equation |
publisher |
Elsevier |
series |
Alexandria Engineering Journal |
issn |
1110-0168 |
publishDate |
2020-12-01 |
description |
In this paper, we are interested in finding the function u(t,x),(t,x)∈[0,T)×Ω from the final data u(T,x)=ϕ(x), satisfies a nonhomogeneous fractional pseudo-parabolic equation. The problem is stable for the cases σ<ν in the sense that the solution of the problem is regularity-loss and we discuss the regularity of the solution to this problem. For the case σ>ν, the problem is ill-posed (in the sense of Hadamard). We propose the general filtering method to regularize this problem. The well-posedness of the regularized problem and some regularity estimates of the regularized solution are obtained. Moreover, error estimates are established under some a priori conditions of the sought solution. The numerical illustrations are given to show the convergence of our method. |
topic |
35K55 35K70 35K92 47A52 47J06 |
url |
http://www.sciencedirect.com/science/article/pii/S1110016820303653 |
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