Abstract
The one-equation advection models that are being used to describe the movement of various animal populations have been extensively investigated over the last decades. Since the theory behind these equations is well known (and can be found in any textbook on hyperbolic conservation laws), our goal here is to give the reader a brief review of this theory (while leaving behind most technical details). This approach will help the reader understand the analytical results presented in the upcoming chapters regarding the existence and the types of patterns displayed by various hyperbolic models for populations dynamics that exist in the literature.
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Eftimie, R. (2018). A Short Introduction to One-Dimensional Conservation Laws. In: Hyperbolic and Kinetic Models for Self-organised Biological Aggregations. Lecture Notes in Mathematics(), vol 2232. Springer, Cham. https://doi.org/10.1007/978-3-030-02586-1_2
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