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We discuss the long-time behaviour of solutions to Smoluchowski's coagulation equation with kernels of homogeneity one, combining formal asymptotics, heuristic arguments based on linearization, and… (More)

In this article we correct the proof of a uniqueness result for self-similar solutions to Smoluchowski's coagulation equation for kernels $K=K(x,y)$ that are homogeneous of degree zero and close to… (More)

Ants are known to be able to find paths of minimal length between the nest and food sources. The deposit of pheromones while they search for food and their chemotactical response to them has been… (More)

Abstract We show the existence of self-similar solutions with fat tails for Smoluchowski's coagulation equation for homogeneous kernels satisfying C 1 ( x − a y b + x b y − a ) ≤ K ( x , y ) ≤ C 2 (… (More)

In this paper we compute asymptotics of solutions of the kinetic Fokker-Planck equation with inelastic boundary conditions which indicate that the solutions are nonunique if $r < r_c$. The… (More)

Abstract In this paper we consider the long-time asymptotics of a linear version of the Smoluchowski equation which describes the evolution of a tagged particle moving in a random distribution of… (More)

In this paper we continue the formal analysis of the long-time asymptotics of the homoenergetic solutions for the Boltzmann equation that we began in [18]. They have the form f (x, v, t) = g (v − L… (More)

We prove that time-periodic solutions arise via Hopf bifurcation in a finite closed system of coagulation-fragmentation equations. The system we treat is a variant of the Becker-Doering equations, in… (More)

ABSTRACTWe prove the existence of a one-parameter family of self-similar solutions with time-dependent tails for Smoluchowski’s coagulation equation, for a class of rate kernels K(x,y) which are… (More)

In this paper we derive matched asymptotic expansions for a solution of the Keller–Segel system in two space dimensions for which the amount of mass aggregation is 8πN, where N = 1, 2, 3, …… (More)