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Hwayeon Ryu : Time-Delayed PDEs with Stochastic Boundary in Mathematical Modeling of Kidney

Motivated by the dynamic feedback systems in the kidney, we consider time-delayed transport equations with stochastic left-hand boundary conditions. We first prove the existence and uniqueness of the steady-state solution for the deterministic case with sufficiently small delay (e.g., zero left-hand boundary). Likewise, we prove those for the stochastic case using the similar analytic techniques. In this talk we will show the process of model formulation with biological motivation and address the role of time-delay and stochastic boundary on the solution behaviors. The talk should be accessible to all graduate students who are familiar with basic ODE theory.

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