A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems

Michael Ortiz; Alexander Mielke

Displaying similar documents to “A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems”

Numerical approaches to rate-independent processes and applications in inelasticity

Alexander Mielke, Tomáš Roubíček (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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A conceptual numerical strategy for rate-independent processes in the energetic formulation is proposed and its convergence is proved under various rather mild data qualifications. The novelty is that we obtain convergence of subsequences of space-time discretizations even in case where the limit problem does not have a unique solution and we need no additional assumptions on higher regularity of the limit solution. The variety of general perspectives thus obtained is illustrated...

Strong minimizers of Blake & Zisserman functional

Michele Carriero, Antonio Leaci, Franco Tomarelli (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Gradient flows of non convex functionals in Hilbert spaces and applications

Riccarda Rossi, Giuseppe Savaré (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert space $ℋ$ $\{\begin{matrix} u^{'} (t) + \partial_{ℓ} φ (u (t)) ∋ f (t) & a.e. in (0, T), u (0) = u_{0}, \end{matrix}$ where $φ : ℋ \to (- \infty, + \infty]$ is a proper, lower semicontinuous functional which is not supposed to be a (smooth perturbation of a) convex functional and $\partial_{ℓ} φ$ is (a suitable limiting version of) its subdifferential. We will present some new existence results for the solutions of the equation by exploiting a technique, featuring some ideas from the theory of and of . Our analysis is also motivated by...