Session S01 - Modeling and Computation for Control and Optimization of Biological and Physical Systems

Wednesday, July 14, 16:30 ~ 16:55 UTC-3

Variational Problems with Distributional and Weak Gradient Constraints

Carlos Rautenberg

George Mason University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We consider variational problems with mixed boundary conditions and (distributional or weak) gradient constraints arising in the growth of non-homogeneous sand piles. In this setting, the upper bound in the constraint is either a function or a Borel measure; this allows the pile growth to observe discontinuities. We address existence and uniqueness of the model under low regularity assumptions, and rigorously identify its Fenchel pre-dual problem. The latter in some cases is posed on a non-standard space of Borel measures with square integrable divergences. We conclude the talk by introducing a mixed finite-element method and several numerical tests .

Joint work with Harbir Antil, Rafael Arndt, and Deepanshu Verma (George Mason University, USA).

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