Rate of convergence to self-similarity for Smoluchowskis coagulation equation with constant coefficientsReportar como inadecuado




Rate of convergence to self-similarity for Smoluchowskis coagulation equation with constant coefficients - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

* Corresponding author 1 Departament de Matemàtiques Barcelona 2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Abstract : 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.

Keywords : Smoluchowski-s equation coagulation equation constant coagulation kernel self-similar variables spectral gap exponential relaxation rate explicit





Autor: José Cañizo - Stéphane Mischler - Clément Mouhot -

Fuente: https://hal.archives-ouvertes.fr/



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