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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 present a model of the full thermo-mechanical evolution of a shape memory body undergoing a uniaxial tensile stress. The well-posedness of the related quasi-static thermo-inelastic problem is addressed by means of hysteresis operators techniques. As a by-product, details on a time-discretization of the problem are provided.
Let L be a nonsymmetric second order uniformly elliptic operator with generalWentzell
boundary conditions. We show that a suitable version of L generates a quasicontractive semigroup
on an Lp space that incorporates both the underlying domain and its boundary. This extends the
earlier work of the authors on the symmetric case.
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