Department of Mathematics,
University of California San Diego
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Math 218: Seminars on Mathematics for Complex Biological Systems
Prof. Pearson Miller
UCSD
Optimal control of weakly nonlinear pattern formation
Abstract:
This talk will present new results on the optimal control of self-organization, motivated by a growing body of empirical work on biological pattern formation in dynamic environments. We pose a boundary control problem for the classic supercritical Turing pattern, asking the best way to reach a non-trivial steady state by controlling the boundary flux of a reactant species. Via the Pontryagin approach, first-order optimality conditions for a generic reaction-diffusion system with a suitable bifurcation structure are derived. Using formal asymptotics, we construct approximate closed-form optimal solutions in feedback law form that are valid for any Turing-unstable system near criticality, which are verified against numerical solutions for a representative reaction-diffusion model.
January 29, 2026
2:00 PM
APM 7321
Research Areas
Mathematical Biology****************************

