Abstract
The chapter provides a variety of existence and uniqueness results for a single 1 − D, first-order, hyperbolic PDEs, which is in feedback interconnection with a system of ODEs. The results are developed for various cases, some of which are not frequently encountered in the literature: Nonlinear and non-local terms as well as distributed and boundary inputs are allowed. The existence/uniqueness results are employed in two applications with non-local terms: A chemical reactor in which an exothermic chemical reaction is taking place and the study of the age distribution of the population of a microorganism.
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Karafyllis I, Krstic M (2017) Stability of integral delay equations and stabilization of age-structured models. ESAIM Control Optim Calc of Var 23(4):1667–1714
Perthame B (2007) Transport equations in biology. Birkhäuser Verlag, Basel
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Karafyllis, I., Krstic, M. (2019). Existence/Uniqueness Results for Hyperbolic PDEs. In: Input-to-State Stability for PDEs. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-91011-6_2
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DOI: https://doi.org/10.1007/978-3-319-91011-6_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91010-9
Online ISBN: 978-3-319-91011-6
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