Gamma-limits and relaxations for rate-independent evolutionary problems

0097225 - ÚTIA 2008 RIV DE eng J - Journal Article
Mielke, A. - Roubíček, Tomáš - Stefannelli, U.
Gamma-limits and relaxations for rate-independent evolutionary problems.
[Gamma limity a uvolnení pro rychlostně nezávislé vývojové úlohy.]
Calculus of Variations and Partial Differential Equations. Roč. 3, č. 31 (2008), s. 387-416. ISSN 0944-2669. E-ISSN 1432-0835
Grant - others:GA MŠk(CZ) LC06052
Program: LC
Institutional research plan: CEZ:AV0Z10750506
Keywords : Rate-independent problems * energetic formulation * Gamma convergence * relaxation * time-incremental minimization
Subject RIV: BA - General Mathematics
Impact factor: 0.912, year: 2008

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.

V praci se vyšetřují Gamma ma limity a uvolnění pro rychlostně nezávislé vyvojové úlohy.
Permanent Link: http://hdl.handle.net/11104/0156413