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- W2024411271 abstract "We prove uniform bounds on moments X_a = sum_{m}{m^a f_m(x,t)} of the Smoluchowski coagulation equations with diffusion, valid in any dimension. If the collision propensities alpha(n,m) of mass n and mass m particles grow more slowly than (n+m)(d(n) + d(m)), and the diffusion rate d(cdot) is non-increasing and satisfies m^{-b_1} leq d(m) leq m^{-b_2} for some b_1 and b_2 satisfying 0 leq b_2 < b_1 < infty, then any weak solution satisfies X_a in L^{infty}(mathbb{R}^d times [0,T]) cap L^1(mathbb{R}^d times [0,T]) for every a in mathbb{N} and T in (0,infty), (provided that certain moments of the initial data are finite). As a consequence, we infer that these conditions are sufficient to ensure uniqueness of a weak solution and its conservation of mass." @default.
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- W2024411271 date "2007-09-25" @default.
- W2024411271 modified "2023-09-23" @default.
- W2024411271 title "Moment Bounds for the Smoluchowski Equation and their Consequences" @default.
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- W2024411271 doi "https://doi.org/10.1007/s00220-007-0304-5" @default.
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