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We investigate a global-in-time variational approach to abstract evolution
by means of the weighted energy-dissipation functionals proposed by Mielke and Ortiz [ESAIM: COCV14 (2008) 494–516]. In particular, we focus on
gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow.
Sharp convergence rates are provided and the convergence analysis is combined with time-discretization....
We investigate a global-in-time variational approach to abstract evolution
by means of the weighted energy-dissipation functionals proposed by Mielke and Ortiz [ESAIM: COCV14 (2008) 494–516]. In particular, we focus on
gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow.
Sharp convergence rates are provided and the convergence analysis is combined with time-discretization....
The work focuses on the Γ-convergence problem and the convergence of minimizers for a functional defined in a periodic perforated medium and
combining the bulk (volume distributed) energy and the surface
energy distributed on the perforation boundary. It is assumed that the mean value
of surface energy at each level set of test function is equal to
zero.
Under natural coercivity and p-growth assumptions on the bulk energy, and the assumption that the surface energy satisfies p-growth upper bound,...
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