Variational Convergence of Gradient Flows and Rate-Independent Evolutions in Metric Spaces

被引：0
作者：
Alexander Mielke
Riccarda Rossi
Giuseppe Savaré
机构：
[1] Weierstras-Institut,Institut für Mathematik
[2] Humboldt-Universität zu Berlin,Dipartimento di Matematica
[3] Università di Brescia,Dipartimento di Matematica “F. Casorati”
[4] Università di Pavia,undefined
来源：
Milan Journal of Mathematics | 2012年 / 80卷
关键词：
Primary 49Q20; Secondary 34A60; Gamma-convergence; doubly nonlinear evolution equations; BV solutions; differential inclusions; viscous regularization; vanishing-viscosity limit;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the asymptotic behaviour of families of gradient flows in a general metric setting, when the metric-dissipation potentials degenerate in the limit to a dissipation with linear growth.
引用
收藏
页码：381 / 410
页数：29
相关论文
共 29 条
[1]  
Ambrosio L.(2009)Existence and stability for Fokker-Planck equations with log-concave reference measure Probab. Theory Relat. Fields 145 517-564
[2]  
Savaré G.(1999)Differentiability of Lipschitz functions on metric measure spaces Geom. Funct. Anal. 9 428-517
[3]  
Zambotti L.(1973)Sulla convergenza degli integrali dell’energia per operatori ellittici del secondo ordine Boll. Un. Mat. Ital. (4) 8 391-411
[4]  
Cheeger J.(2006)On the rate–independent limit of systems with dry friction and small viscosity J. Convex Analysis 13 151-167
[5]  
De Giorgi E.(2012)BV solutions and viscosity approximations of rateindependent systems ESAIM Control Optim. Calc. Var. 18 36-80
[6]  
Spagnolo S.(2008)Γ-limits and relaxations for rate-independent evolutionary problems Calculus of Variations and Partial Differential Equations 31 387-416
[7]  
Efendiev M.(1969)Convergence of convex sets and of solutions of variational inequalities Advances in Math. 3 510-585
[8]  
Mielke A.(2010)From diffusion to reaction via Γ-convergence SIAM J. Math. Anal. 42 1805-1825
[9]  
Mielke A.(2005)Multiscale modeling for the bioelectric activity of the heart SIAM J. Math. Anal. 37 1333-1370
[10]  
Rossi R.(2008)A metric approach to a class of doubly nonlinear evolution equations and applications Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 7 97-169
123