A Uniqueness Result for Self-Similar Profiles to Smoluchowski’s Coagulation Equation Revisited

Grain growth for astrophysics with discontinuous Galerkin schemes

“…Explicit solutions exist only for the so-called constant (Smoluchowski 1916;Schumann 1940;Scott 1968), additive (Golovin 1963;Scott 1968) and multiplicative kernels (McLeod 1962a;Scott 1968), implying numerical resolution for physical problems. Among the known solutions, self-similar solutions are particularly important since they provide asymptotic behaviour of the mass distribution at large times (Schumann 1940;Friedlander & Wang 1966;Wang 1966;Menon & Pego 2004;Niethammer et al 2016;Laurençot 2018). A generic feature of these solutions is the exponentially fast decay of the solution at large masses.…”

Uniqueness of Mass-Conserving Self-similar Solutions to Smoluchowski’s Coagulation Equation with Inverse Power Law Kernels

“…by (21), we realize that h 1 * H 1 − h 2 * H 2 = (h 1 + h 2 ) * E − E. Inserting this formula in (23), we end up with…”

Contractivity for Smoluchowski's coagulation equation with solvable kernels

“…Similar norms have also been used in [12, 14] to prove the uniqueness of self‐similar profiles for perturbations of the constant kernel.…”

“…We state here a first obvious result where the uniqueness property u = 0 comes from the fact that both L and B are one-to-one: Similar norms have also been used in [12,14] to prove the uniqueness of self-similar profiles for perturbations of the constant kernel.…”