Self-similar solutions to a coagulation equation with multiplicative kernel

Abstract

Existence of self-similar solutions to the Oort-Hulst-Safronov coagulation equation with multiplicative coagulation kernel is established. These solutions are given by s(t) −τ ψ τ (y/s(t)) for (t, y) ∈ (0, T ) × (0, ∞), where T is some arbitrary positive real number, s(t) = ((3 − τ )(T − t)) −1/(3−τ ) and the parameter τ ranges in a given interval [τ c , 3). In addition, the second moment of these self-similar solutions blows up at time T . As for the profile ψ τ , it belongs to L 1 (0, ∞; y 2 dy) for each τ ∈ [τ c , 3) but its behaviour for small and large y varies with the parameter τ . MSC 2000: 45J05, 34C11

Existence and Uniqueness of Mass Conserving Solutions to Safronov-Dubovski Coagulation Equation for Product Kernel

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Finite volume approximation of nonlinear agglomeration population balance equation on triangular grid

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Mathematical Aspects of Coagulation-Fragmentation Equations

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