Smoothing and decay estimates for nonlinear diffusion equations : equations of porous medium type

By Juan Luis V'azquez. 2006

549 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/807114fa45625b45bf1d8ce6b96d0e71c60a0cac

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Option pricing with linear market impact and nonlinear Black–Scholes equations (2018, unknown): “As will be discussed hereafter, these results can be seen as related to regularity results concerning porous media equations (see the book by Vazquez [39] for a complete reference), in particular in the case of Fast Diffusion Equations, as well as the papers by Crandall and Pierre [11, 13] about int”
Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations (2008, unknown): “See also monographs [29] and [30] by Vazquez.”
The classification of locally conformally flat Yamabe solitons (2011, background): “The existence of such solutions is proven in [14] (Proposition 7.”
A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains (2013, background): “As in the standard Laplacian case, we expect the estimates to be considerably different, leading to phenomena like finite-time extinction, see [6, 7, 9, 10, 44].”
Local Aronson–Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds (2008, unknown): “[11,33].”
The Fisher–KPP problem with doubly nonlinear “fast” diffusion (2016, methodology): “p-Laplacian) is much used in the elliptic and parabolic literature (see [17, 21, 27, 39, 44, 53, 54] and their references) and allows to recover the Porous Medium operator choosing p = 2 or the p-Laplacian operator choosing m = 1.”
Recent progress in the theory of Nonlinear Diffusion with Fractional Laplacian Operators (2014, methodology): “Our calculation of a priori estimates with exact exponents and best constants is closely related to the sharp decay estimate for solutions of the porous medium/fast diffusion equation in [89, 90].”
Fast diffusion flow on manifolds of nonpositive curvature (2008, unknown): “[18].”
Nonlinear flows and rigidity results on compact manifolds (2013, background): “Higher order regularity results follow: see for instance [58] in the Euclidean case.”
Asymptotics of the Fast Diffusion Equation via Entropy Estimates (2007, methodology): “Such approach has been consistently used in [49] where it is shown that the effect on the self-similar solutions of Barenblatt type is just to eliminate the denominator m in (2) and (5).”
Total Variation Flow and Sign Fast Diffusion in one dimension (2011, background): “(See also [14, 21, 22] and the book [25] for a complete theory of the logarithmic diffusion equation in one space dimension for positive initial data.”
Classical solutions and higher regularity for nonlinear fractional diffusion equations (2013, background): “If the function φ satisfies the condition φ(u) ≥ C|u| for every u ∈ R and some fixed m > 0, a classical scaling argument allows to obtain a decay estimate for every t > 0; see for instance [23].”
Porous media equations with two weights: smoothing and decay properties of energy solutions via Poincar\'e inequalities (2012, background): “For a thorough analysis of smoothing and decay properties of solutions to large classes of nonlinear evolution equations on RN , see the monograph [52] (see also [26]).”