Constructive stability results in interpolation inequalities and explicit improvements of decay rates of fast diffusion equations
Bonforte, Matteo; Dolbeault, Jean; Nazaret, Bruno; Simonov, Nikita (2023), Constructive stability results in interpolation inequalities and explicit improvements of decay rates of fast diffusion equations, Discrete and Continuous Dynamical Systems. Series A, 43, 3&4, p. 1070-1089. 10.3934/dcds.2022093
View/ Open
Type
Article accepté pour publication ou publiéDate
2023Journal name
Discrete and Continuous Dynamical Systems. Series AVolume
43Number
3&4Pages
1070-1089
Publication identifier
Metadata
Show full item recordAuthor(s)
Bonforte, MatteoUniversidad Autónoma de Madrid [UAM]
Dolbeault, Jean

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Nazaret, Bruno
Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) [SAMM]
Simonov, Nikita

Laboratoire de Mathématiques et Modélisation d'Evry [LaMME]
Abstract (EN)
We provide a scheme of a recent stability result for a family of Gagliardo-Nirenberg-Sobolev (GNS) inequalities, which is equivalent to an improved entropy-entropy production inequality associated with an appropriate fast diffusion equation (FDE) written in self-similar variables. This result can be rephrased as an improved decay rate of the entropy of the solution of (FDE) for well prepared initial data. There is a family of Caffarelli-Kohn-Nirenberg (CKN) inequalities which has a very similar structure. When the exponents are in a range for which the optimal functions for (CKN) are radially symmetric, we investigate how the methods for (GNS) can be extended to (CKN). In particular, we prove that the solutions of the evolution equation associated to (CKN) also satisfy an improved decay rate of the entropy, after an explicit delay. However, the improved rate is obtained without assuming that initial data are well prepared, which is a major difference with the (GNS) case.Subjects / Keywords
Gagliardo-Nirenberg-Sobolev inequality; Caffarelli-Kohn-Nirenberg inequality; stability; entropy methods; fast diffusion equation; Harnack Principle; self-similar solutions; Hardy-Poincaré inequalities; spectral gap; rates of convergenceRelated items
Showing items related by title and author.
-
Bonforte, Matteo; Dolbeault, Jean; Nazaret, Bruno; Simonov, Nikita (2020) Document de travail / Working paper
-
Bonforte, Matteo; Dolbeault, Jean; Muratori, Matteo; Nazaret, Bruno (2017) Article accepté pour publication ou publié
-
Bonforte, Matteo; Dolbeault, Jean; Nazaret, Bruno; Simonov, Nikita (2022) Document de travail / Working paper
-
Bonforte, Matteo; Dolbeault, Jean; Nazaret, Bruno; Simonov, Nikita (2020) Document de travail / Working paper
-
Bonforte, Matteo; Dolbeault, Jean; Muratori, Matteo; Nazaret, Bruno (2017) Article accepté pour publication ou publié