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Weighted energy-dissipation functionals for gradient flows

Alexander Mielke, Ulisse Stefanelli (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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....

Well-posedness of a thermo-mechanical model for shape memory alloys under tension

Pavel Krejčí, Ulisse Stefanelli (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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.

Wentzell Boundary Conditions in the Nonsymmetric Case

A. Favini, G. R. Goldstein, J. A. Goldstein, S. Romanelli (2008)

Mathematical Modelling of Natural Phenomena

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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