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

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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 languageEnglish
Article number108209
JournalApplied Mathematics Letters
Volume132
DOIs
Publication statusPublished - Oct 2022

Keywords

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

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