Visintin, A. Mathematical models of hysteresis. (English) Zbl 0656.73043 Topics in nonsmooth mechanics, 295-326 (1988). [For the entire collection see Zbl 0646.00014.] Hysteretic effects are considered here with the help of Volterra-like functionals, i.e. functionals depending on the past history. The classical Duhem-Madelung and Preisach models of hysteresis are introduced. Following the work of Krasnosel’skij, existence theorems are presented for some examples ranging from ferromagnetism, biological models and plasticity to surface tension at solid liquid interfaces. Reviewer: H.Matthies Cited in 17 Documents MSC: 74S30 Other numerical methods in solid mechanics (MSC2010) 74S99 Numerical and other methods in solid mechanics 74F15 Electromagnetic effects in solid mechanics 74L15 Biomechanical solid mechanics 74A15 Thermodynamics in solid mechanics 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 47A53 (Semi-) Fredholm operators; index theories Keywords:Volterra-like functionals; Duhem-Madelung and Preisach models; existence theorems Citations:Zbl 0575.35045; Zbl 0608.65082; Zbl 0573.34016; Zbl 0576.35103; Zbl 0646.00014 PDF BibTeX XML OpenURL