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arXiv · 2406.00897

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

Christopher N. Angstmann·Stuart-James M. Burney·Daniel S. Han·Bruce I. Henry·Zhuang Xu
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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.

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Christopher N. Angstmann, Stuart-James M. Burney, Daniel S. Han, Bruce I. Henry, Zhuang Xu. 2024-06-02. Exact Solutions of Time-Delay Integer- and Fractional-Order Advection Equations. https://arxiv.org/abs/2406.00897

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