2011
DOI: 10.4310/cms.2011.v9.n2.a2
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Entropies for radially symmetric higher-order nonlinear diffusion equations

Abstract: 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.Key words. Higher-order diffusion equations, thin-film equation, quantum diffusion model, po… Show more

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Cited by 8 publications
(12 citation statements)
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“…It is well known for the fourth-order equation (3), that weak solutions may not be unique [13]. We expect the same phenomenon to occur for (1).…”
Section: Theoremsupporting
confidence: 70%
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“…It is well known for the fourth-order equation (3), that weak solutions may not be unique [13]. We expect the same phenomenon to occur for (1).…”
Section: Theoremsupporting
confidence: 70%
“…are spaces of functions that are 1-periodic in each spatial coordinate direction. The derivation of the sixth-order equation 1in [3] was performed on R d and hence, it does not include the derivation of physically relevant boundary conditions. In this work, we have chosen periodic boundary conditions to simplify the analysis.…”
Section: Theorem 1 (Global Existence Of Weak Solutionsmentioning
confidence: 99%
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