Maximum principle for time-fractional parabolic equations with a reaction coefficient of arbitrary sign

Natalia Kopteva

doi:10.1016/j.aml.2022.108209

Maximum principle for time-fractional parabolic equations with a reaction coefficient of arbitrary sign

Natalia Kopteva

Research output: Contribution to journal › Article › peer-review

Abstract

We consider time-fractional parabolic equations with a Caputo time derivative of order α∈(0,1). For such equations, we give an elementary proof of the weak maximum principle under no assumptions on the sign of the reaction coefficient. This proof is also extended for weak solutions, as well as for various types of boundary conditions and variable-coefficient variable-order multiterm time-fractional parabolic equations.

Original language	English
Article number	108209
Journal	Applied Mathematics Letters
Volume	132
DOIs	https://doi.org/10.1016/j.aml.2022.108209
Publication status	Published - Oct 2022

Keywords

Reaction coefficient of arbitrary sign
Subdiffusion,
Time-fractional parabolic equations
Weak maximum principle
Weak solutions

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10.1016/j.aml.2022.108209

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title = "Maximum principle for time-fractional parabolic equations with a reaction coefficient of arbitrary sign",

abstract = "We consider time-fractional parabolic equations with a Caputo time derivative of order α∈(0,1). For such equations, we give an elementary proof of the weak maximum principle under no assumptions on the sign of the reaction coefficient. This proof is also extended for weak solutions, as well as for various types of boundary conditions and variable-coefficient variable-order multiterm time-fractional parabolic equations.",

keywords = "Reaction coefficient of arbitrary sign, Subdiffusion,, Time-fractional parabolic equations, Weak maximum principle, Weak solutions",

author = "Natalia Kopteva",

note = "Publisher Copyright: {\textcopyright} 2022 The Author(s)",

year = "2022",

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doi = "10.1016/j.aml.2022.108209",

language = "English",

volume = "132",

journal = "Applied Mathematics Letters",

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AU - Kopteva, Natalia

PY - 2022/10

Y1 - 2022/10

N2 - We consider time-fractional parabolic equations with a Caputo time derivative of order α∈(0,1). For such equations, we give an elementary proof of the weak maximum principle under no assumptions on the sign of the reaction coefficient. This proof is also extended for weak solutions, as well as for various types of boundary conditions and variable-coefficient variable-order multiterm time-fractional parabolic equations.

AB - We consider time-fractional parabolic equations with a Caputo time derivative of order α∈(0,1). For such equations, we give an elementary proof of the weak maximum principle under no assumptions on the sign of the reaction coefficient. This proof is also extended for weak solutions, as well as for various types of boundary conditions and variable-coefficient variable-order multiterm time-fractional parabolic equations.

KW - Reaction coefficient of arbitrary sign

KW - Subdiffusion,

KW - Time-fractional parabolic equations

KW - Weak maximum principle

KW - Weak solutions

UR - https://www.scopus.com/pages/publications/85131373433

U2 - 10.1016/j.aml.2022.108209

DO - 10.1016/j.aml.2022.108209

M3 - Article

AN - SCOPUS:85131373433

SN - 0893-9659

VL - 132

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 108209

ER -

Maximum principle for time-fractional parabolic equations with a reaction coefficient of arbitrary sign

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Keywords

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