Communications in Mathematical Sciences
Volume 9 (2011)
Entropies for radially symmetric higher-order nonlinear diffusion equations
Pages: 353 – 382
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.
higher-order diffusion equations, thin-film equation, quantum diffusion model, polynomial decision problem, quantifier elimination
2010 Mathematics Subject Classification
35B45, 35G25, 35K55, 76A20, 82C70