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

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10.4310/cms.2011.v9.n2.a2

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AU - Jüngel, Ansgar

AU - Matthes, Daniel

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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 - https://www.scopus.com/pages/publications/78650438615

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Entropies for radially symmetric higher-order nonlinear diffusion equations

Abstract

Keywords

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