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Pressureless Euler alignment system with control
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DOI：10.1142/S0218202518400018.png)
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摘要
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We study a non-local hydrodynamic system with control. First, we characterize the control dynamics as a sub-optimal approximation to the optimal control problem constrained to the evolution of the pressureless Euler alignment system. We then discuss the critical thresholds that lead to global regularity or finite-time blow-up of strong solutions in one and two dimensions. Finally, we use a finite volume scheme, coupled with an implicit-explicit time integrator to solve numerically the stiff scale of the controlled system. Several numerical simulations are shown to validate the theoretical and computational results of the paper.
Keyword:
Self-organization
hydrodynamic models
finite volume methods
critical thresholds
optimal control
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