Parabolic problems with the Preisach hysteresis operator in boundary conditions

Abstract

MSC: 35K15 47J40 45M15 35B41 Keywords: Thermocontrol problem Hysteresis Preisach operator Periodicity Global attractorParabolic initial boundary-value problems coupled (via the boundary condition) with ordinary differential equations whose righthand side contains the Preisach hysteresis operator are considered. In particular, these problems model thermocontrol processes in chemical reactors, climate-control systems, biological cells, etc. For the Preisach operator with and without time delay, solvability, periodicity of solutions, and global B-attractors are studied.

Mathematical analysis and numerical solution of models with dynamic Preisach hysteresis

“…In recent years, mathematical analysis of rate-independent models of hysteresis coupled with partial differential equations has been progressing; see among others the works by Visintin [41,42], Eleuteri [15,16], Showalter [39], Bermúdez [4], Krejčí [24] and Brokate and Sprekels [11], Mielke [33], Gurevich [18]. for a physical point of view.…”

Periodic solutions to a class of biological diffusion models with hysteresis effect

“…Hysteresis phenomena occur in many fields such as phase transitions, superconductivity and biology [10][11][12][13][14]. According to [14], the hysteresis is referred to as a rate independent memory effect and hysteresis operator becomes an important concept to analyze the mathematical properties of some hysteresis models (see [11,[15][16][17]). As pointed out by Visintin in [14] that some kinds of hysteresis operators can be represented by ordinary differential inclusion containing subdifferential of the indicator function of a closed interval.…”

The model of closed-loop control by thermostats: properties and numerical simulations

“…[8], [13], [5]. in [3], [11], [6] processes described by semilinear equations were controlled by thermostats. In [12] a control by thermostats for linear heat flow was considered.…”