Dynamical Scaling in Smoluchowski's Coagulation Equations: Uniform Convergence
نویسندگان
چکیده
منابع مشابه
Dynamical Scaling in Smoluchowski's Coagulation Equations: Uniform Convergence
We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski’s coagulation equations for the solvable kernels K(x, y) = 2, x+ y and xy. We prove the uniform convergence of densities to the self-similar solution with exponential tails under the regularity hypothesis that a suitable moment have an integrable Fourier transform. For the discrete equations we prove uniform conv...
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Abstract We establish nearly optimal rates of convergence to self-similar solutions of Smoluchowski’s coagulation equation with kernels K = 2, x + y, and xy. The method is a simple analogue of the Berry-Esséen theorems in classical probability and requires minimal assumptions on the initial data, namely that of an extra finite moment condition. For each kernel it is shown that the convergence r...
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ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2005
ISSN: 0036-1410,1095-7154
DOI: 10.1137/s0036141003430263