Nonlocal final value problem governed by semilinear anomalous diffusion equations

Dinh-Ke Tran; Tran-Phuong-Thuy Lam

doi:10.3934/eect.2020038

Article Contents

2020, Volume 9, Issue 3: 891-914. Doi: 10.3934/eect.2020038

This issue Previous Article On the management fourth-order Schrödinger-Hartree equation Next Article

Nonlocal final value problem governed by semilinear anomalous diffusion equations

Dinh-Ke Tran^1, , and
Tran-Phuong-Thuy Lam^2,

1.
Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
2.
Department of Mathematics, Electric Power University, 235 Hoang Quoc Viet, Hanoi, Vietnam

^* Corresponding author: Dinh-Ke TRAN (ketd@hnue.edu.vn)
^* Corresponding author: Dinh-Ke TRAN (ketd@hnue.edu.vn)

Received: May 31, 2019

Revised: October 31, 2019

Early access: March 2020

Published: September 2020

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Abstract

Our goal is to establish some sufficient conditions for the solvability of the nonlocal final value problem involving a class of partial differential equations, which describes the anomalous diffusion phenomenon. Our analysis is based on the theory of completely positive functions, resolvent operators and fixed point arguments in suitable function spaces. Especially, utilizing the regularity of resolvent operators, we are able to deal with non-Lipschitz cases. The obtained results, in particular, extend recent ones proved for fractional diffusion equations.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 45D05; 45K05.

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References

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