Communications in Mathematical Sciences

Volume 9 (2011)

Number 2

Entropies for radially symmetric higher-order nonlinear diffusion equations

Pages: 353 – 382

DOI: https://dx.doi.org/10.4310/CMS.2011.v9.n2.a2

Authors

Mario Bukal (Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria)

Ansgar Jüngel (Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria)

Daniel Matthes (Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria)

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, thin-film equation, quantum diffusion model, polynomial decision problem, quantifier elimination

2010 Mathematics Subject Classification

35B45, 35G25, 35K55, 76A20, 82C70

Published 21 December 2010