Periodic Solutions of Parabolic Equations with Hysteresis in Dimension 1

Periodic Wave Shock solutions of Burgers equations

In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY

Well-posedness of parabolic equations containing hysteresis with diffusive thresholds

In the paper, we develop a theory of reaction-diffusion equations containing discontinuous hysteresis operator — the so-called non-ideal relay. The nonideal relay (or a bi-stable relay, or lazy switch) is the most basic, yet nontrivial hysteresis operator. The state (output) of the non-ideal relay switches from −1 to 1 when the input exceeds a threshold value x ∈ R and switches back to state −1...

Parabolic Pde with Hysteresis

Our objective here is to describe some results on the well-posedness of initial-boundary-value problems for a nonlinear parabolic partial diierential equation with memory eeects and with general boundary conditions. The system consists of a general porous medium equation together with a family of ordinary diierential equations subject to constraints. Such a system includes a very general class ...

PERIODIC SOLUTIONS IN CERTAIN CLASS OF 3- DIMENSION DISCONTINUOUS AUTONOMOUS SYSTEMS

In the present paper the linear oscillator in R3 with z =constanthas been considered. The aim is to determine the necessary conditions forthe persistence of periodic solutions under discontinuous perturbations. A newapproach based on a computational method has been used. At the end weapply our method on an example.