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We approximate, in the sense of
Γ-convergence, free-discontinuity functionals with linear
growth in the gradient by a sequence of non-local integral
functionals depending on the average of the gradients on small
balls. The result extends to higher dimension what we already proved in
the one-dimensional case.
In this work we deal with the numerical solution of a
Hamilton-Jacobi-Bellman (HJB) equation with infinitely many
solutions. To compute the maximal solution – the optimal
cost of the original optimal control problem – we present a
complete discrete method based on the use of some finite elements
and penalization techniques.
We deal with practical aspects of an approach to the numerical realization of optimal shape design problems, which is based on a combination of the fictitious domain method with the optimal control approach. Introducing a new control variable in the right-hand side of the state problem, the original problem is transformed into a new one, where all the calculations are performed on a fixed domain. Some model examples are presented.
We introduce a modification of the Monge–Kantorovitch problem of exponent 2 which accommodates non balanced initial and final densities. The augmented lagrangian numerical method introduced in [6] is adapted to this “unbalanced” problem. We illustrate the usability of this method on an idealized error estimation problem in meteorology.
We introduce a modification of the Monge–Kantorovitch
problem of exponent 2 which accommodates non balanced initial
and final densities. The augmented Lagrangian numerical method
introduced in [6] is adapted to this “unbalanced”
problem. We illustrate the usability of this method on an
idealized error estimation problem in meteorology.
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