Abstract
Partial differential equations describe numerous phenomena in nature, technology, medicine, economics, ... In this first chapter we shall describe the derivation of the partial differential equations associated with several prominent examples, using the laws of nature and mathematical facts. One calls such a derivation (mathematical) modeling.
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Notes
- 1.
Here \({\mathrm{sech}}(x)=\cosh ^{-1}(x)\) denotes the hyperbolic secant function.
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Arendt, W., Urban, K. (2023). Modeling, or where do differential equations come from. In: Partial Differential Equations. Graduate Texts in Mathematics, vol 294. Springer, Cham. https://doi.org/10.1007/978-3-031-13379-4_1
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DOI: https://doi.org/10.1007/978-3-031-13379-4_1
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