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

页码：1519 / 1537

页数：19

共 50 条

[1] On the Dirichlet problem for the nonlinear diffusion equation in non-smooth domains
Abdulla, UG
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 260 (02) : 384 - 403
[2] Smooth and non-smooth traveling wave solutions of a class of nonlinear dispersive equation
Zhao, Xiaoshan
Wu, Aidi
He, Wenzhang
[J]. CHAOS SOLITONS & FRACTALS, 2009, 41 (04) : 2168 - 2177
[3] STRUCTURE AND REGULARITY OF THE GLOBAL ATTRACTOR OF A REACTION-DIFFUSION EQUATION WITH NON-SMOOTH NONLINEAR TERM
Kapustyan, Oleksiy V.
Kasyanov, Pavlo O.
Valero, Jose
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, 34 (10) : 4155 - 4182
[4] The Helmholtz equation in a non-smooth inclusion
Yan, Guozheng
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (09) : 2825 - 2832
[5] Smooth and non-smooth traveling waves in a nonlinearly dispersive equation
Li, JB
Liu, ZR
[J]. APPLIED MATHEMATICAL MODELLING, 2000, 25 (01) : 41 - 56
[6] On nonlinear inclusions in non-smooth domains
Ben-El-Mechaiekh H.
[J]. Arabian Journal of Mathematics, 2012, 1 (4) : 395 - 416
[7] Behavior of the solution of nonlinear hyperbolic equation in a domain with non-smooth boundary
Hajiev, T. S.
Rasulov, R. A.
[J]. APPLIED MATHEMATICS LETTERS, 2011, 24 (03) : 283 - 287
[8] An optimal error estimate for the two-dimensional nonlinear time fractional advection-diffusion equation with smooth and non-smooth solutions
Zhang, Hui
Jia, Junqing
Jiang, Xiaoyun
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 79 (10) : 2819 - 2831
[9] Non-invasive feedback stabilization of smooth and non-smooth nonlinear systems
Abeloos, G.
Collette, C.
Kerschen, G.
[J]. PROCEEDINGS OF INTERNATIONAL CONFERENCE ON NOISE AND VIBRATION ENGINEERING (ISMA2020) / INTERNATIONAL CONFERENCE ON UNCERTAINTY IN STRUCTURAL DYNAMICS (USD2020), 2020, : 2107 - 2116
[10] Smooth and non-smooth travelling waves in a nonlinearly dispersive Boussinesq equation
Shen, JW
Xu, W
Lei, YM
[J]. CHAOS SOLITONS & FRACTALS, 2005, 23 (01) : 117 - 130

← 1 2 3 4 5 →