• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail - No thumbnail

Rate of convergence to self-similarity for Smoluchowski's coagulation equation with constant coefficients

Cañizo, José Alfredo; Mischler, Stéphane; Mouhot, Clément (2010), Rate of convergence to self-similarity for Smoluchowski's coagulation equation with constant coefficients, SIAM Journal on Mathematical Analysis, 41, 6, p. 2283-2314. http://dx.doi.org/10.1137/08074091X

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00337661/en/
Date
2010
Journal name
SIAM Journal on Mathematical Analysis
Volume
41
Number
6
Publisher
SIAM
Pages
2283-2314
Publication identifier
http://dx.doi.org/10.1137/08074091X
Metadata
Show full item record
Author(s)
Cañizo, José Alfredo
Mischler, Stéphane
Mouhot, Clément
Abstract (EN)
We show that solutions to Smoluchowski's equation with a constant coagulation kernel and an initial datum with some regularity and exponentially decaying tail converge exponentially fast to a self-similar profile. This convergence holds in a weighted Sobolev norm which implies the L² convergence of derivatives up to a certain order k depending on the regularity of the initial condition. We prove these results through the study of the linearized coagulation equation in self-similar variables, for which we show a spectral gap in a scale of weighted Sobolev spaces. We also take advantage of the fact that the Laplace or Fourier transforms of this equation can be explicitly solved in this case.
Subjects / Keywords
Smoluchowski's equation; coagulation equation; constant coagulation kernel; self-similar variables; spectral gap; exponential relaxation rate; explicit

Related items

Showing items related by title and author.

  • Thumbnail
    Rate of convergence to self-similarity for the fragmentation equation in L1 spaces 
    Caceres, Maria J.; Cañizo, José Alfredo; Mischler, Stéphane (2010) Communication / Conférence
  • Thumbnail
    Regularity, local behavior and partial uniqueness for self-similar profiles of Smoluchowski's coagulation equation 
    Mischler, Stéphane; Cañizo, José Alfredo (2011) Article accepté pour publication ou publié
  • Thumbnail
    Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations 
    Mischler, Stéphane; Cañizo, José Alfredo; Caceres, Maria J. (2011) Article accepté pour publication ou publié
  • Thumbnail
    Stability, convergence to self-similarity and elastic limit for the Boltzmann equation for inelastic hard spheres 
    Mouhot, Clément; Mischler, Stéphane (2009) Article accepté pour publication ou publié
  • Thumbnail
    Dust and self-similarity for the Smoluchowski coagulation equation 
    Escobedo, Miguel; Mischler, Stéphane (2006) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo