Entropies for radially symmetric higher-order nonlinear diffusion equations

Mario Bukalt; Ansgar Jüngel; Daniel Matthes

doi:10.4310/cms.2011.v9.n2.a2

Entropies for radially symmetric higher-order nonlinear diffusion equations

Mario Bukalt, Ansgar Jüngel, Daniel Matthes

Technical University of Vienna

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	353-382
Number of pages	30
Journal	Communications in Mathematical Sciences
Volume	9
Issue number	2
DOIs	https://doi.org/10.4310/cms.2011.v9.n2.a2
State	Published - Jun 2011
Externally published	Yes

Keywords

Higher-order diffusion equations
Polynomial decision problem
Quantifier elimination
Quantum diffusion model
Thin-film equation

Access to Document

10.4310/cms.2011.v9.n2.a2

Cite this

@article{0746f4922a8446e4af6b21040323530f,

title = "Entropies for radially symmetric higher-order nonlinear diffusion equations",

abstract = "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.",

keywords = "Higher-order diffusion equations, Polynomial decision problem, Quantifier elimination, Quantum diffusion model, Thin-film equation",

author = "Mario Bukalt and Ansgar J{\"u}ngel and Daniel Matthes",

year = "2011",

month = jun,

doi = "10.4310/cms.2011.v9.n2.a2",

language = "English",

volume = "9",

pages = "353--382",

journal = "Communications in Mathematical Sciences",

issn = "1539-6746",

publisher = "International Press of Boston, Inc.",

number = "2",

}

TY - JOUR

T1 - Entropies for radially symmetric higher-order nonlinear diffusion equations

AU - Bukalt, Mario

AU - Jüngel, Ansgar

AU - Matthes, Daniel

PY - 2011/6

Y1 - 2011/6

N2 - 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.

AB - 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.

KW - Higher-order diffusion equations

KW - Polynomial decision problem

KW - Quantifier elimination

KW - Quantum diffusion model

KW - Thin-film equation

UR - http://www.scopus.com/inward/record.url?scp=78650438615&partnerID=8YFLogxK

U2 - 10.4310/cms.2011.v9.n2.a2

DO - 10.4310/cms.2011.v9.n2.a2

M3 - Article

AN - SCOPUS:78650438615

SN - 1539-6746

VL - 9

SP - 353

EP - 382

JO - Communications in Mathematical Sciences

JF - Communications in Mathematical Sciences

IS - 2

ER -

Entropies for radially symmetric higher-order nonlinear diffusion equations

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this