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

2021/03/11 by Yuri Luchko, Luchko, Yuri, Anna Suzuki +3
Mathematics · #26A33 #35A05 #35B30 #35B50 #35C05 #35E05 #35L05 #45K05 #60E99 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2103.06582

openalex publication_date 2021/03/11 · openalex created_date 2021/03/15 · openalex updated_date 2026/08/01

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.

Citations

• Fractional Differential Equations

Related

• Maximum principles for a time-space fractional diffusion equation
• Maximum principle and its application for the nonlinear time-fractional diffusion equations with Cauchy-Dirichlet conditions
• Studies on an inverse source problem for a space-time fractional diffusion equation by constructing a strong maximum principle
• Maximum principle for time-fractional parabolic equations with a reaction coefficient of arbitrary sign
• On a multi-dimensional transport equation with nonlocal velocity and fractional dissipation