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On a class of partial differntial equations with hysteresis arising in magnetohydrodynamics
In this paper we deal with a class of parabolic partial differential equations containing a continuous hysteresis operator. We get an existence result by means of a technique based on an implicit time discretization scheme and we also analyse the dependence of the solution on the data. This model equation appears in the context of magnetohydrodynamics.
Asymptotic behavior of a Neumann parabolic problem with hysteresis
A parabolic equation in two or three space variables with a Preisach hysteresis operator and with homogeneous Neumann boundary conditions is shown to admit a unique global regular solution. A detailed investigation of the Preisach memory dynamics shows that the system converges to an equilibrium in the state space of all admissible Preisach memory configurations as time tends to infinity.
Well posedness results for a class of partial differential equations with hysteresis arising in electromagnetism
We consider an evolutionary P.D.E. motivated by models for electromagnetic processes in ferromagnetic materials. Magnetic hysteresis is represented by means of a hysteresis operator. Under suitable assumptions, an existence and uniqueness theorem is obtained, together with the Lipschitz continuous dependence on the data and some further regularity results. The discussion of the behaviour of the solution in dependence on physical parameters of the problem is also outlined.
Existence of solutions to a two-dimensional model for nonisothermal two-phase flows of incompressible fluids
We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. The model was recently introduced in [12] where existence of weak solutions was proved in three space dimensions. Here, we aim at studying the properties of solutions in the two-dimensional case. In particular, we can show existence of global in time solutions satisfying a stronger formulation of the model with respect to the one considered in [12]. Moreover, we can admit slightly more general conditions on some material coefficients of the system.
Magnetohydrodynamic flow with hysteresis
We consider a model system describing the 2D flow of a conducting fluid surrounded by a ferromagnetic solid under the influence of the hysteretic response of the surrounding medium. We assume that this influence can be represented by the Preisach hysteresis operator. Existence and uniqueness of solutions for the resulting system of PDEs with hysteresis nonlinearities is established in the convexity domain of the Preisach operator.
Asymptotic convergence results for a system of partial differential equations with hysteresis
A partial differential equation motivated by electromagnetic field equations in ferromagnetic media is considered with a relaxed rate dependent constitutive relation. It is shown that the solutions converge to the unique solution of the limit parabolic problem with a rate independent Preisach hysteresis constitutive operator as the relaxation parameter tends to zero.