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Bibliografie

Journal Article

Gamma-limits and relaxations for rate-independent evolutionary problems

Mielke A., Roubíček Tomáš, Stefannelli U.

: Calculus of Variations and Partial Differential Equations vol.3, 31 (2008), p. 387-416

: CEZ:AV0Z10750506

: LC06052, GA MŠk

: Rate-independent problems, energetic formulation, Gamma convergence, relaxation, time-incremental minimization

(eng): This work uses the energetic formulation of rate-independent systems that is based on the stored-energy functionals $/calE$ and the dissipation distance $/calD$. For sequences $(/calE_k)_{k/in /N}$ and $(/calD_k)_{k/in /N}$ we address the question under which conditions the limits $q_/infty$ of solutions $q_k:[0,T]/to /calQ$ satisfy a suitable limit problem with limit functionals $/calE_/infty$ and $/calD_/infty$, which are the corresponding $/Gamma$-limits. We derive a sufficient condition, called /emph{conditional upper semi-continuity of the stable sets}, which is essential to guarantee that $q_/infty$ solves the limit problem. In particular, this condition holds if certain /emph{joint recovery sequences} exist. Moreover, we show that time-incremental minimization problems can be used to approximate the solutions.

(cze): V praci se vyšetřují Gamma ma limity a uvolnění pro rychlostně nezávislé vyvojové úlohy.

: BA