Exact Solutions of Time-Delay Integer- and Fractional-Order Advection Equations

2024/06/02 by Angstmann, Christopher N., Burney, Stuart-James M., Han, Daniel S. +2
#33E20 #34K06 #35C10 #35F10 #42A38 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.00897

Abstract

Transport phenomena play a vital role in various fields of science and engineering. In this work, exact solutions are derived for advection equations with integer- and fractional-order time derivatives and a constant time-delay in the spatial derivative. Solutions are obtained, for arbitrary separable initial conditions, by incorporating recently introduced delay functions in a separation of variables approach. Examples are provided showing oscillatory and translatory behaviours that are fundamentally different to standard propagating wave solutions.

Related

• Finite Time Blowup of Integer- and Fractional-Order Time-Delayed Diffusion Equations
• The exact solutions of differential equation with delay
• The radiative transport equation with waiting time and its diffusion approximation with a time-fractional derivative
• Advection equation analysed by two-timing method
• Features of the fractional diffusion-advection equation