On existence and regularity of a terminal value problem for the time fractional diffusion equation

Nguyen Huy Tuan; Tran Bao Ngoc; Yong Zhou; Donal O'Regan

doi:10.1088/1361-6420/ab730d

On existence and regularity of a terminal value problem for the time fractional diffusion equation

Nguyen Huy Tuan
, Tran Bao Ngoc
, Yong Zhou
, Donal O'Regan

Mathematics

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

23 Citations (Scopus)

Abstract

In this paper we consider a final value problem for a diffusion equation with time-space fractional differentiation on a bounded domain D of R^k, k ≥ 1, which includes the fractional power L^β, 0 < β ≤ 1, of a symmetric uniformly elliptic operator L defined on L ²(D). A representation of solutions is given by using the Laplace transform and the spectrum of L^β. We establish some existence and regularity results for our problem in both the linear and nonlinear case.

Original language	English
Article number	055011
Journal	Inverse Problems
Volume	36
Issue number	5
DOIs	https://doi.org/10.1088/1361-6420/ab730d
Publication status	Published - May 2020

Keywords

existence and regularity
final value problem
time fractional derivative
uniqueness

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10.1088/1361-6420/ab730d

Cite this

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abstract = "In this paper we consider a final value problem for a diffusion equation with time-space fractional differentiation on a bounded domain D of Rk, k ≥ 1, which includes the fractional power Lβ, 0 < β ≤ 1, of a symmetric uniformly elliptic operator L defined on L 2(D). A representation of solutions is given by using the Laplace transform and the spectrum of Lβ. We establish some existence and regularity results for our problem in both the linear and nonlinear case.",

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AU - Tuan, Nguyen Huy

AU - Ngoc, Tran Bao

AU - Zhou, Yong

AU - O'Regan, Donal

PY - 2020/5

Y1 - 2020/5

N2 - In this paper we consider a final value problem for a diffusion equation with time-space fractional differentiation on a bounded domain D of Rk, k ≥ 1, which includes the fractional power Lβ, 0 < β ≤ 1, of a symmetric uniformly elliptic operator L defined on L 2(D). A representation of solutions is given by using the Laplace transform and the spectrum of Lβ. We establish some existence and regularity results for our problem in both the linear and nonlinear case.

AB - In this paper we consider a final value problem for a diffusion equation with time-space fractional differentiation on a bounded domain D of Rk, k ≥ 1, which includes the fractional power Lβ, 0 < β ≤ 1, of a symmetric uniformly elliptic operator L defined on L 2(D). A representation of solutions is given by using the Laplace transform and the spectrum of Lβ. We establish some existence and regularity results for our problem in both the linear and nonlinear case.

KW - existence and regularity

KW - final value problem

KW - time fractional derivative

KW - uniqueness

UR - https://www.scopus.com/pages/publications/85084637083

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DO - 10.1088/1361-6420/ab730d

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VL - 36

JO - Inverse Problems

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M1 - 055011

ER -

On existence and regularity of a terminal value problem for the time fractional diffusion equation

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Keywords

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