Exact Solutions of Time-Delay Integer- and Fractional-Order Advection Equations
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910617781141504 |
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| author | Angstmann, Christopher N. Burney, Stuart-James M. Han, Daniel S. Henry, Bruce I. Xu, Zhuang |
| author_facet | Angstmann, Christopher N. Burney, Stuart-James M. Han, Daniel S. Henry, Bruce I. Xu, Zhuang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00897 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact Solutions of Time-Delay Integer- and Fractional-Order Advection Equations Angstmann, Christopher N. Burney, Stuart-James M. Han, Daniel S. Henry, Bruce I. Xu, Zhuang Analysis of PDEs 35C10, 35F10, 34K06, 42A38, 33E20 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. |
| title | Exact Solutions of Time-Delay Integer- and Fractional-Order Advection Equations |
| topic | Analysis of PDEs 35C10, 35F10, 34K06, 42A38, 33E20 |
| url | https://arxiv.org/abs/2406.00897 |