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whereand⋐are concentric parabolic cylinders. This also implies that time derivative exists as an-function, which is not evident directly by the definition. Corollary 1.2 (Time derivative) Let. Letbe a viscosity solution to the generalp-parabolic Eq. (1.1). Ifpandsatisfy one of the following ...
The computations are related to a test of positivity of the intrinsic second order derivative or a test of singularity of the extremal flow. We derive an algorithm called COTCOT (Conditions of Order Two and COnjugate Times), available on the web, and apply it to the minimal time problem of...
end of the air test, the waveguide completely lost its waveguiding ability, and the laser beam was mostly diffused into the neighboring region of the waveguide. These results indicate that the CLD chromophore does not survive operation in air, but can survive for very long time when oxygen is...
It is based on recent theoretical developmentsof geometric optimal control, and the article contains a reviewof second order optimality conditions.The computations are related to a testof positivity of the intrinsic second order derivative or a test ofsingularity of the extremal flow. We derive an ...