Periodic solutions of partial differential equations with hysteresis
Weak stabilization of solutions to PDEs with hysteresis in thermovisco-elastoplasticity
The impact of uncertain parameters on ratchetting trends in hypoplasticity
Perturbed parameters are considered in a hypoplastic model of granular materials. For fixed parameters, the model response to a periodic stress loading and unloading converges to a limit state of strain. The focus of this contribution is the assessment of the change in the limit strain caused by varying model parameters.
Modelled behaviour of granular material during loading and unloading
The main aim of this paper is to analyze numerically the model behaviour of a granular material during loading and unloading. The model was originally proposed by D. Kolymbas and afterward modified by E. Bauer. For our purposes the constitutive equation was transformed into a rate independent form by introducing a dimensionless time parameter. By this transformation we were able to derive explicit formulas for the strain-stress trajectories during loading-unloading cycles and compare the results...
Hysteresis and Periodic Solutions of Semilinear and Quasilinear Wave Equations.
Periodic Solutions to a Parabolic Equation with Hysteresis.
Periodic solutions to Maxwell equations in nonlinear media
Editorial comment on the paper Huashui Zhan, Junning Zhao: Some remarks on Prandtl system
Modelling of singularities in elastoplastic materials with fatigue
The hypothesis that, on the macroscopic level, the accumulated fatigue of an elastoplastic material with kinematic hardening can be identified from the mathematical point of view with the dissipated energy, is used for the construction of a new constitutive elastoplastic fatigue model. Its analytical investigation characterizes conditions for the formation of singularities in a finite time. The corresponding constitutive law is then coupled with the dynamical equation of motion of a one-dimensional...
A remark on the local Lipschitz continuity of vector hysteresis operators
It is known that the vector stop operator with a convex closed characteristic of class is locally Lipschitz continuous in the space of absolutely continuous functions if the unit outward normal mapping is Lipschitz continuous on the boundary of . We prove that in the regular case, this condition is also necessary.
Resonance in Preisach systems
This paper deals with the asymptotic behavior as of solutions to the forced Preisach oscillator equation , , where is a Preisach hysteresis operator, is a given function and is the time variable. We establish an explicit asymptotic relation between the Preisach measure and the function (or, in a more physical terminology, a balance condition between the hysteresis dissipation and the external forcing) which guarantees that every solution remains bounded for all times. Examples show...
Otto Vejvoda passed away
On Maxwell equations with the Preisach hysteresis operator: The one- dimensional time-periodic case
Energy functionals for the Preisach hysteresis operator are used for proving the existence of weak periodic solutions of the one-dimensional systems of Maxwell equations with hysteresis for not too large right-hand sides. The upper bound for the speed of propagation of waves is independent of the hysteresis operator.
Hysteresis memory preserving operators
The recent development of mathematical methods of investigation of problems with hysteresis has shown that the structure of the hysteresis memory plays a substantial role. In this paper we characterize the hysteresis operators which exhibit a memory effect of the Preisach type (memory preserving operators). We investigate their properties (continuity, invertibility) and we establish some relations between special classes of such operators (Preisach, Ishlinskii and Nemytskii operators). For a general...
Forced periodic vibrations of an elastic system with elastico-plastic damping
We prove the existence and find necessary and sufficient conditions for the uniqueness of the time-periodic solution to the equations for an arbitrary (sufficiently smooth) periodic right-hand side , where denotes the Laplace operator with respect to , and is the Ishlinskii hysteresis operator. For this equation describes e.g. the vibrations of an elastic membrane in an elastico-plastic medium.
On Ishlinskij's model for non-perfectly elastic bodies
The main goal of the paper is to formulate some new properties of the Ishlinskii hysteresis operator , which characterizes e.g. the relation between the deformation and the stress in a non-perfectly elastic (elastico-plastic) material. We introduce two energy functionals and derive the energy inequalities. As an example we investigate the equation describing the motion of a mass point at the extremity of an elastico-plastic spring.
A monotonicity method for solving hyperbolic problems with hysteresis
Periodic solutions of a class of abstract nonlinear equations of the second order
On solvability of equations of the th order with jumping nonlinearities
Hysteresis operators - a new approach to evolution differential inequalities
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