Discrete dynamics of complex bodies with substructural dissipation: Variational integrators and convergence
Matteo Focardi Paolo Maria Mariano
Discrete & Continuous Dynamical Systems - B 2009, 11(1): 109-130 doi: 10.3934/dcdsb.2009.11.109
For the linearized setting of the dynamics of complex bodies we construct variational integrators and prove their convergence by making use of BV estimates on the rate fields. We allow for peculiar substructural inertia and internal dissipation, all accounted for by a d'Alembert-Lagrange-type principle.
keywords: dynamical systems asynchronous variational integrators convergence Complex bodies
On a 1-capacitary type problem in the plane
Matteo Focardi Maria Stella Gelli Giovanni Pisante
Communications on Pure & Applied Analysis 2010, 9(5): 1319-1333 doi: 10.3934/cpaa.2010.9.1319
We study a $1$-capacitary type problem in $R^2$: given a set $E$, we minimize the perimeter (in the sense of De Giorgi) among all the sets containing $E$ (modulo $H^1$) and satisfying an indecomposability constraint (according to the definition by [1]. By suitably choosing the representant of the relevant set $E$, we show that a convexification process characterizes the minimizers.
    As a consequence of our result we determine the $1$-capacity of (a suitable representant of) sets with finite perimeter in the plane.
keywords: capacity Perimeter indecomposable sets.

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