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We show how to design them such that they are sufficiently regular (not continuous but L∞) We then establish closed-loop stability, regularity of control, and regularity of solutions of the PDE.
We then establish closed-loop stability, regularity of control, and regularity of solutions of the PDE.
Due to the existence of boundary layer or interior layer for the state and adjoint state as well as limited regularity of control variable, we derive a posteriori error estimates for the state and adjoint state, which can be utilized to guide the mesh refinements in the adaptive algorithm.
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Listen to the regularity of the control of Tennyson's pentameter lines from the opening of his short poem "Ulysses,".
Here piecewise constant FE space is used for the approximation of the control due to the limited regularity of the optimal control (normally, (H^{1})).
Due to the limited regularity of the optimal control u in general, we therefore only consider a piecewise constant space.
Indeed, from (2.22) and (2.25) we can observe that the regularity of the optimal control (u^) agrees with that of the adjoint state (z^).
Due to the limited regularity of the optimal control u in general, there will be no advantage in considering higher-order finite element spaces rather than the piecewise constant space for the control.
Simulation results show the regularity of energy consumption with the control variables.
In fact, SK currents have been demonstrated to control the regularity of spontaneous activity in SNc dopaminergic neurons from both juvenile and mature animals in vitro (Ping and Shepard, 1996; Wolfart et al., 2001).
Sesion 9: Regularity of habits Session 10: Stress-control Session 11: Prolem-solving strategies Session 12: Final session.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com