We illustrate an alternative derivation of the viscous regulariza- tion of a nonlinear forward-backward diffusion equation which was studied in [A. Novick-Cohen and R. L. Pego. Trans. Amer. Math. Soc., 324:331{351]. We propose and discuss a new on-smooth" variant of the viscous regulariza- tion and we offer an heuristic argument that indicates that this variant should display interesting hysteretic efiects. Finally, we offer a constructive proof of existence of solutions for the viscous regularization based on a suitable approx- imation scheme.
Tomassetti, G. (2017). Smooth and non-smooth regularizations of the nonlinear diffusion equation. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 10(6), 1519-1537 [10.3934/dcdss.2017078].
Smooth and non-smooth regularizations of the nonlinear diffusion equation
Tomassetti G.
2017-01-01
Abstract
We illustrate an alternative derivation of the viscous regulariza- tion of a nonlinear forward-backward diffusion equation which was studied in [A. Novick-Cohen and R. L. Pego. Trans. Amer. Math. Soc., 324:331{351]. We propose and discuss a new on-smooth" variant of the viscous regulariza- tion and we offer an heuristic argument that indicates that this variant should display interesting hysteretic efiects. Finally, we offer a constructive proof of existence of solutions for the viscous regularization based on a suitable approx- imation scheme.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
