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We consider differentiability issues associated to the problem of minimizingthe accumulation of a granular cohesionless material on a certain surface. Thedesign variable or control is determined by source locations and intensitythereof. The control problem is described by an optimization problem infunction space and constrained by a variational inequality or a non-smoothequation. We address a regularization approach via a family of nonlinearpartial differential equations, and provide a novel result of Newtondifferentiability of the control-to-state map. Further, we discuss solutionalgorithms for the state equation as well as for the optimization problem.

Differentiability and Control of a Model for Granular Material Accumulation