A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy
Alice Fiaschi (2009)
Annales de l'I.H.P. Analyse non linéaire
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Alice Fiaschi (2009)
Annales de l'I.H.P. Analyse non linéaire
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Martin Kružík, Johannes Zimmer (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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Rate-independent problems are considered, where the stored energy density is a function of the gradient. The stored energy density may not be quasiconvex and is assumed to grow linearly. Moreover, arbitrary behaviour at infinity is allowed. In particular, the stored energy density is not required to coincide at infinity with a positively 1-homogeneous function. The existence of a rate-independent process is shown in the so-called energetic formulation.
Piera, Francisco J., Mazumdar, Ravi R. (2008)
Electronic Journal of Probability [electronic only]
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Tomáš Roubíček (1997)
Commentationes Mathematicae Universitatis Carolinae
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The Young measures, used widely for relaxation of various optimization problems, can be naturally understood as certain functionals on suitable space of integrands, which allows readily various generalizations. The paper is focused on such functionals which can be attained by sequences whose “energy” (=th power) does not concentrate in the sense that it is relatively weakly compact in . Straightforward applications to coercive optimization problems are briefly outlined.
Jiří Jarušek (1990)
Commentationes Mathematicae Universitatis Carolinae
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Christian Heinemann, Christiane Kraus (2014)
Mathematica Bohemica
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This paper addresses analytical investigations of degenerating PDE systems for phase separation and damage processes considered on nonsmooth time-dependent domains with mixed boundary conditions for the displacement field. The evolution of the system is described by a degenerating Cahn-Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a quasi-static balance equation for the displacement field. The analysis is performed on a...