IRIS

Global existence and long-time behavior of solutions to a family of nonlinear fourth order evolution equations on the d-dimensional euclidean space are studied. Among them, for suitable values of the parameters we obtain a quantum drift diffusion model, and a thin film type equation. These equations constitute gradient flows for the perturbed information functionals with respect to the L^2-Wasserstein metric.

A Family of Nonlinear Fourth Order Equations of Gradient Flow Type

SAVARE', GIUSEPPE
2009-01-01

Abstract

Global existence and long-time behavior of solutions to a family of nonlinear fourth order evolution equations on the d-dimensional euclidean space are studied. Among them, for suitable values of the parameters we obtain a quantum drift diffusion model, and a thin film type equation. These equations constitute gradient flows for the perturbed information functionals with respect to the L^2-Wasserstein metric.
2009
The Mathematics category includes resources dealing with mathematics, applied mathematics, statistics and probability.
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
sì
WOS:000274421200003
2-s2.0-74949092030
Sì, ma tipo non specificato
Inglese
Internazionale
STAMPA
34
11
1352
1397
46
This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the disgression of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering. 2008 Impact Factor: 1.242 Ranking: 30/175 in Mathematics, Applied; 20/214 in Mathematics 2008 5-Year Impact Factor: 1.329 Mathematical Citation Quotient for 2008: 1.24 (The 2008 All Journal MCQ is 0.26). MCQ is an index provided by the American Mathematical Society
Entropy method; Fourth-order equations; Gradient flow; Nonlinear parabolic equations; Wasserstein distance; Optimal transport
http://www.imati.cnr.it/~savare/pubblicazioni/McCann-Matthes-Savare09.pdf
3
info:eu-repo/semantics/article
262
Mccann, Robert; Matthes, Daniel; Savare', Giuseppe
1 Contributo su Rivista::1.1 Articolo in rivista
none
1.1 Articolo in rivista
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/203073
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 127
  • ???jsp.display-item.citation.isi??? 119
social impact