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Global solutions to the multicomponent Smoluchowski coagulation equation are constructed for measure-valued initial data with minimal assumptions on the moments. The framework is based on an abstract formulation of the Arzel\`a-Ascoli…

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-Ess\'een theorem in classical…

We consider mass-conserving self-similar solutions for Smoluchowski's coagulation equation with kernel $K(\xi,\eta)= (\xi \eta)^{\lambda}$ with $\lambda \in (0,1/2)$. It is known that such self-similar solutions $g(x)$ satisfy that…

We show the existence of self-similar solutions with fat tails for Smoluchowski's coagulation equation for homogeneous kernels satisfying $C_1 \left(x^{-a}y^{b}+x^{b}y^{-a}\right)\leq K\left(x,y\right)\leq…

In this article we study an extension of Smoluchowski's discrete coagulation equation, where particle in- and output takes place. This model is frequently used to describe aggregation processes in combination with sedimentation of clusters.…

Sufficient conditions are given for existence and uniqueness in Smoluchowski's coagulation equation, for a wide class of coagulation kernels and initial mass distributions. An example of non-uniqueness is constructed. The stochastic…

We study the solutions of the Smoluchowski coagulation equation with a regularisation term which removes clusters from the system when their mass exceeds a specified cut-off size, M. We focus primarily on collision kernels which would…

Uniqueness of mass-conserving self-similar solutions to Smoluchowski's coagulation equation is shown when the coagulation kernel $K$ is given by $K(x,x\_*)=2(x x\_*)^{-\alpha}$, $(x,x\_*)\in (0,\infty)^2$, for some $\alpha>0$.

This article is devoted to a generalized version of Smoluchowski's coagulation equation. This model describes the time evolution of a system of aggregating particles under the effect of external input and output particles. We show that for…

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…

In this paper we show how the method of Zakharov transformations may be used to analyze the stationary solutions of the Smoluchowski aggregation equation for arbitrary homogeneous kernel. The resulting massdistributions are of Kolmogorov…

We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski's equations of coagulation for the solvable kernels $K(x,y)=2$, $x+y$ and $xy$. In addition to the known self-similar solutions with exponential tails, there…

In this paper we study a class of coagulation equations including a source term that injects in the system clusters of size of order one. The coagulation kernel is homogeneous, of homogeneity $\gamma < 1$, such that $K(x,y)$ is…

We study multicomponent coagulation via the Smoluchowski coagulation equation under non-equilibrium stationary conditions induced by a source of small clusters. The coagulation kernel can be very general, merely satisfying certain power law…

We propose an efficient and fast numerical algorithm of finding a \emph{stationary} solution of large systems of aggregation-fragmentation equations of Smoluchowski type for concentrations of reacting particles. This method is applicable…

It is well known that for a large class of coagulation kernels, Smoluchowski coagulation equations have particular power law solutions which yield a constant flux of mass along all scales of the system. In this paper, we prove that for some…

Motivated by the recent results of Andreis-Iyer-Magnanini (2023), we provide a short proof, revisiting the one of Escobedo-Mischler-Perthame (2002), that for a large class of coagulation kernels, any weak solution to the Smoluchowski…

We demonstrate an approach to solving the coagulation equation that involves using a finite number of moments of the particle size distribution. This approach is particularly useful when only general properties of the distribution, and…

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 numerical simulations. The case of what we…

The existence of self-similar solutions with fat tails for Smoluchowski's coagulation equation has so far only been established for the solvable and the diagonal kernel. In this paper we prove the existence of such self-similar solutions…