IRREVERSIBILITY AND HYSTERESIS FOR A FORWARD–BACKWARD DIFFUSION EQUATION

Source abstract

Our intention in this paper is to publicize and extend somewhat important work of Plotnikov 7 on the asymptotic limits of solutions of viscous regularizations of a nonlinear diffusion PDE with a cubic nonlinearity. Since the formal limit PDE is in general ill-posed, we expect that the limit solves instead a corresponding diffusion equation with hysteresis effects. We employ entropy/entropy flux pairs to prove various assertions consistent with this expectation.