On the maximum principle for the multi-term fractional transport equation

Yuri Luchko; Anna Suzuki; Masahiro Yamamoto

doi:10.1016/j.jmaa.2021.125579

On the maximum principle for the multi-term fractional transport equation

Yuri Luchko, Anna Suzuki, Masahiro Yamamoto

IFS - Creative Flow Research Division

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5 Citations (Scopus)

Abstract

In this paper, we prove a maximum principle for the general multi-term space-time-fractional transport equation and apply it for establishing uniqueness of solution to an initial-boundary-value problem for this equation. We also derive some comparison principles for solutions to the initial-boundary-value problems with different problem data. Finally, we present a maximum principle for the Cauchy problem for a time-fractional transport equation on an unbounded domain.

Original language	English
Article number	125579
Journal	Journal of Mathematical Analysis and Applications
Volume	505
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2021.125579
Publication status	Published - 2022 Jan

Keywords

Cauchy problem
Comparison principle
Initial-boundary-value problem
Maximum principle
Space-time-fractional multi-term transport equation
Time-fractional transport equation

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10.1016/j.jmaa.2021.125579

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title = "On the maximum principle for the multi-term fractional transport equation",

abstract = "In this paper, we prove a maximum principle for the general multi-term space-time-fractional transport equation and apply it for establishing uniqueness of solution to an initial-boundary-value problem for this equation. We also derive some comparison principles for solutions to the initial-boundary-value problems with different problem data. Finally, we present a maximum principle for the Cauchy problem for a time-fractional transport equation on an unbounded domain.",

keywords = "Cauchy problem, Comparison principle, Initial-boundary-value problem, Maximum principle, Space-time-fractional multi-term transport equation, Time-fractional transport equation",

author = "Yuri Luchko and Anna Suzuki and Masahiro Yamamoto",

note = "Funding Information: The third named author was supported by Grant-in-Aid for Scientific Research (S) 15H05740 and Grant-in-Aid (A) 20H00117 of Japan Society for the Promotion of Science and by the National Natural Science Foundation of China (no. 11771270 , 91730303 ). This work was curried out with the support of the RUDN University Strategic Academic Leadership Program . Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

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doi = "10.1016/j.jmaa.2021.125579",

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AU - Luchko, Yuri

AU - Suzuki, Anna

AU - Yamamoto, Masahiro

N1 - Funding Information: The third named author was supported by Grant-in-Aid for Scientific Research (S) 15H05740 and Grant-in-Aid (A) 20H00117 of Japan Society for the Promotion of Science and by the National Natural Science Foundation of China (no. 11771270 , 91730303 ). This work was curried out with the support of the RUDN University Strategic Academic Leadership Program . Publisher Copyright: © 2021 Elsevier Inc.

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Y1 - 2022/1

N2 - In this paper, we prove a maximum principle for the general multi-term space-time-fractional transport equation and apply it for establishing uniqueness of solution to an initial-boundary-value problem for this equation. We also derive some comparison principles for solutions to the initial-boundary-value problems with different problem data. Finally, we present a maximum principle for the Cauchy problem for a time-fractional transport equation on an unbounded domain.

AB - In this paper, we prove a maximum principle for the general multi-term space-time-fractional transport equation and apply it for establishing uniqueness of solution to an initial-boundary-value problem for this equation. We also derive some comparison principles for solutions to the initial-boundary-value problems with different problem data. Finally, we present a maximum principle for the Cauchy problem for a time-fractional transport equation on an unbounded domain.

KW - Cauchy problem

KW - Comparison principle

KW - Initial-boundary-value problem

KW - Maximum principle

KW - Space-time-fractional multi-term transport equation

KW - Time-fractional transport equation

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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On the maximum principle for the multi-term fractional transport equation

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Keywords

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