Evolution of rate-independent systems. (English) Zbl 1120.47062

Mielke, Alexander

Dafermos, C.M.(ed.) et al., Evolutionary equations. Vol. II. Amsterdam: Elsevier/North-Holland (ISBN 0-444-52048-1/hbk). Handbook of Differential Equations, 461-559 (2005).

In this chapter of the Handbook of Differential Equations, a unified approach to rate-independent evolutionary systems is suggested. This new energetic approach combines in a natural way different aspects of rate-independent models or hysteresis operators in the context of continuum mechanics. The final section presents a selection of applications, which illustrates the abstract theory developed in the previous sections.
For the entire collection see [Zbl 1074.35003].

Reviewer: Evgeniy Panov (Novgorod)

MSC:

47N20	Applications of operator theory to differential and integral equations
47J40	Equations with nonlinear hysteresis operators
47J20	Variational and other types of inequalities involving nonlinear operators (general)
74C15	Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74N30	Problems involving hysteresis in solids
35Q72	Other PDE from mechanics (MSC2000)
34G25	Evolution inclusions
35-00	General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to partial differential equations
35B35	Stability in context of PDEs
35K85	Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
74H99	Dynamical problems in solid mechanics

Keywords:

rate-independent systems; hysteresis operators; energetic formulation