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
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Article accepté pour publication ou publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00337661/en/Date
2010Journal name
SIAM Journal on Mathematical AnalysisVolume
41Number
6Publisher
SIAM
Pages
2283-2314
Publication identifier
Metadata
Show full item recordAbstract (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; explicitRelated items
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Caceres, Maria J.; Cañizo, José Alfredo; Mischler, Stéphane (2010) Communication / Conférence
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