ENTROPIES FOR RADIALLY SYMMETRIC HIGHER-ORDER NONLINEAR DIFFUSION EQUATIONS

被引：0

作者：

Bukal, Mario ^{[1
]}

Juengel, Ansgar ^{[1
]}

Matthes, Daniel ^{[1
]}

机构：

[1] Vienna Univ Technol, Inst Anal & Sci Comp, A-1040 Vienna, Austria

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2011年 / 9卷 / 02期

基金：

奥地利科学基金会;

关键词：

Higher-order diffusion equations; thin-film equation; quantum diffusion model; polynomial decision problem; quantifier elimination; PARABOLIC EQUATION; FLUCTUATIONS; EXISTENCE; INTERFACE;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A previously developed algebraic approach to proving entropy production inequalities is extended to deal with radially symmetric solutions for a class of higher-order diffusion equations in multiple space dimensions. In application of the method, novel a priori estimates are derived for the thin-film equation, the fourth-order Derrida-Lebowitz-Speer-Spohn equation, and a sixth-order quantum diffusion equation.

引用

页码：353 / 382

页数：30

共 50 条

[1] A HYBRID METHOD FOR HIGHER-ORDER NONLINEAR DIFFUSION EQUATIONS
Kim, Junseok
Sur, Jeanman
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2005, 20 (01): : 179 - 193
[2] ADI schemes for higher-order nonlinear diffusion equations
Witelski, TP
Bowen, M
APPLIED NUMERICAL MATHEMATICS, 2003, 45 (2-3) : 331 - 351
[3] On radially symmetric solutions of second and higher order nonlinear partial differential equations
Goyal, Sulbha
Goyal, Vinod
MATHEMATICAL INEQUALITIES & APPLICATIONS, 2006, 9 (02): : 303 - 324
[4] On a sequence of higher-order nonlinear diffusion-convection equations
Charalambous, Kyriakos
Sophocleous, Christodoulos
32ND INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (GROUP32), 2019, 1194
[5] An algorithmic construction of entropies in higher-order nonlinear PDEs
Jüngel, A
Matthes, D
NONLINEARITY, 2006, 19 (03) : 633 - 659
[6] HIGHER-ORDER NONLINEAR DISPERSIVE EQUATIONS
KENIG, CE
PONCE, G
VEGA, L
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 122 (01) : 157 - 166
[7] Oscillation of higher-order nonlinear difference equations
Grace, SR
Lalli, BS
MATHEMATICAL AND COMPUTER MODELLING, 2005, 41 (4-5) : 485 - 491
[8] HIGHER-ORDER NONLINEAR DEGENERATE PARABOLIC EQUATIONS
BERNIS, F
FRIEDMAN, A
JOURNAL OF DIFFERENTIAL EQUATIONS, 1990, 83 (01) : 179 - 206
[9] SOME HIGHER-ORDER NONLINEAR EVOLUTION EQUATIONS
HABERMAN, R
STUDIES IN APPLIED MATHEMATICS, 1975, 54 (04) : 275 - 282
[10] The oscillation of higher-order nonlinear difference equations
Wu, W
Zhang, BG
APPLIED MATHEMATICS LETTERS, 2004, 17 (12) : 1363 - 1370

← 1 2 3 4 5 →