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The Age-Structured Chemostat with Substrate Dynamics as a Control System
Iasson Karafyllis, Dionysis Theodosis, Miroslav Krstic
https://arxiv.org/abs/2511.09963 https://arxiv.org/pdf/2511.09963 https://arxiv.org/html/2511.09963
arXiv:2511.09963v1 Announce Type: new
Abstract: In this work we study an age-structured chemostat model with a renewal boundary condition and a coupled substrate equation. The model is nonlinear and consists of a hyperbolic partial differential equation and an ordinary differential equation with nonlinear, nonlocal terms appearing both in the ordinary differential equation and the boundary condition. Both differential equations contain a non-negative control input, while the states of the model are required to be positive. Under an appropriate weak solution framework, we determine the state space and the input space for this model. We prove global existence and uniqueness of solutions for all admissible initial conditions and all allowable control inputs. To this purpose we employ a combination of Banach's fixed-point theorem with implicit solution formulas and useful solution estimates. Finally, we show that the age-structured chemostat model gives a well-defined control system on a metric space.
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They learned from the Grifter-in-Chief.
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https://www.nytimes.com/2025/08/31/us/politics/trump-jan-6-rioters-compensation.html

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M\'aty\'as Domokos
https://arxiv.org/abs/2509.03223 https://arxiv.org/pdf/2509.03223

On the cones of classical groups
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https://open.spotify.com/track/0HcjuZfdMuKHCspb20Pshj

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— one with equal rights, material prosperity, and commitment to human progress
— will require our government, culture, politics, and people to recom…

The Argument | Substack
Join Us. We're Libbing Out. Click to read The Argument, a Substack publication.