Outwards pointing hysteresis operators and asymptotic behaviour of evolution equations
Copyright policy )Outwards pointing hysteresis operators and asymptotic behaviour of evolution equations
The paper deals with the long-time behaviour of evolution systems described by ODEs and PDEs with hysteresis operators. The analysis is based on two concepts. The first one is the outward pointing property of the involved hysteresis operators which implies uniform a priori bounds for solutions, the second one is related to the hysteresis modelling itself and consists in introducing a class of thermodynamically consistent generalized Prandtl-Ishlinskii operators as a model for a nonlinear elastoplastic material law. A stability result for solutions in one-dimensional visco-elasto-plasticity is derived as an illustration of the theory.
- Leibniz Association Germany
- Czech Academy of Sciences Czech Republic
- Weierstrass Institute for Applied Analysis and Stochastics Germany
- Weierstrass Institute Germany
ddc:510, hysteresis operators -- Prandtl-Ishlinskii operator -- asymptotic behaviour -- visco-elasto-plasticity, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Asymptotic behavior of solutions to PDEs, asymptotic behaviour, 35B40, article, 74K05, Problems involving hysteresis in solids, hysteresis operators, 74N30, 34C55, 35K60, Hysteresis for ordinary differential equations, Prandtl-Ishlinskii operator, 510, Equations with nonlinear hysteresis operators, Strings, visco-elasto-plasticity, 47J40
ddc:510, hysteresis operators -- Prandtl-Ishlinskii operator -- asymptotic behaviour -- visco-elasto-plasticity, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Asymptotic behavior of solutions to PDEs, asymptotic behaviour, 35B40, article, 74K05, Problems involving hysteresis in solids, hysteresis operators, 74N30, 34C55, 35K60, Hysteresis for ordinary differential equations, Prandtl-Ishlinskii operator, 510, Equations with nonlinear hysteresis operators, Strings, visco-elasto-plasticity, 47J40
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