Fine Asymptotics for Fast Diffusion Equations

By José Antonio Carrillo, Juan Luis V'azquez. 2003

103 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/06c300a7e5f06fe71ab883fa0a5d9ce9074b36b5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds (2008, methodology): “The entropy method has lately been used in many situations: nonlinear diffusion equations (such as fast diffusions [7, 6], equations of fourth order [2], Landau equation [11], etc.”
Asymptotics of the Fast Diffusion Equation via Entropy Estimates (2007, methodology): “Since much is known in the case m > mc, see for instance [16, 25] and [10, 11, 13, 14, 15, 27, 36, 45] for more complete results, the main novelty of our paper is concerned with the lower range m ≤ mc, which has several interesting new features.”
Hardy-Poincaré inequalities and applications to nonlinear diffusions (2007, unknown): “Lorsque m ∈ [(d − 1)/d, 1) et m ∈ (mc, (d − 1)/d), mc := (d − 2)/d, on renverra respectivement à [9] et [4].”
Exponential decay toward equilibrium via entropy methods for reaction–diffusion equations (2006, methodology): “The entropy method has lately been used in many situations: nonlinear diffusion equations (such as fast diffusions [9,10], equations of fourth order [5], Landau equation [13], etc.”
Special Fast Diffusion with Slow Asymptotics: Entropy Method and Flow on a Riemannian Manifold (2008, unknown): “also [7], [9], [12], [14], [16], [20], [22], [24], [26].”
Functional inequalities, thick tails and asymptotics for the critical mass Patlak–Keller–Segel model (2010, methodology): “Note that if (2.2) holds for µ and ν, it also holds if we change µ and ν by multiplying them by a positive constant, i.e., ∇ϕ#(µ/M) = (ν/M) if and only if ∇ϕ#µ = ν.”
Nonlinear flows and rigidity results on compact manifolds (2013, background): “In the framework of diffusion equations from the PDE point of view we primarily refer to [3] in the linear case, and to [29, 34, 30, 28] for fast diffusion equations in the Euclidean space.”
Global positivity estimates and Harnack inequalities for the fast diffusion equation (2006, unknown): “[10].”