SMOOTH AND NON-SMOOTH REGULARIZATIONS OF THE NONLINEAR DIFFUSION EQUATION

被引：5
|
作者：
Tomassetti, Giuseppe [1 ]
机构：
[1] Roma Tre Univ, Dept Engn, Civil Engn Sect, Via Vito Volterra 62, I-00152 Rome, Italy
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2017年 / 10卷 / 06期
关键词：
Diffusion; backward-parabolic partial differential equations; viscosity; hysteresis; CAHN-HILLIARD EQUATION; BACKWARD PARABOLIC EQUATIONS; PSEUDOPARABOLIC REGULARIZATION; THERMOMECHANICS; THERMODYNAMICS; BEHAVIOR; SYSTEM; LIMIT; HEAT;
D O I：
10.3934/dcdss.2017078
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We illustrate an alternative derivation of the viscous regularization 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 "non-smooth" variant of the viscous regularization and we offer an heuristic argument that indicates that this variant should display interesting hysteretic effects. Finally, we offer a constructive proof of existence of solutions for the viscous regularization based on a suitable approximation scheme.
引用
收藏
页码：1519 / 1537
页数：19
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