Related papers: Self-similar solutions with fat tails for Smolucho…
We consider Smoluchowski's coagulation equation with a kernel of the form $K = 2 + \epsilon W$, where $W$ is a bounded kernel of homogeneity zero. For small $\epsilon$, we prove that solutions approach a universal, unique self-similar…
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 work, we consider self-similar profiles for Smoluchowski's coagulation equation for kernels which are possibly unbounded perturbations of the constant one. For this model, we show that the self-similar solutions for the perturbed…
We show that the Smoluchowski coagulation equation with the solvable kernels $K(x,y)$ equal to $2$, $x+y$ or $xy$ is contractive in suitable Laplace norms. In particular, this proves exponential convergence to a self-similar profile in…
Global weak solutions to the continuous Smoluchowski coagulation equation (SCE) are constructed for coagulation kernels featuring an algebraic singularity for small volumes and growing linearly for large volumes, thereby extending previous…
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 study the long-time behaviour of the solutions to Smoluchowski coagulation equations with a source term of small clusters. The source drives the system out-of-equilibrium, leading to a rich range of different possible long-time…
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…
In this paper we study the fundamental solution of the equation obtained by the linearisation of the Smoluchowski coagulation equation with the multiplicative kernel $(x y)^{\lambda/2}$ with $\lambda\in (1, 2)$ around the steady state…
We construct a time-dependent solution to the Smoluchowski coagulation equation with a constant flux of dust particles entering through the boundary at zero. The dust is instantaneously converted into particles and flux solutions have…
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…
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…
Existence and non-existence of integrable stationary solutions to Smoluchowski's coagulation equation with source are investigated when the source term is integrable with an arbitrary support in (0, $\infty$). Besides algebraic upper and…
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 prove uniqueness of measure solutions for a multi-component version of Smoluchowski's coagulation equation. The result is valid for a broad range of coagulation kernels and allows to include a source term. The classical coagulation…
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 construct a family of self-similar solutions with fat tails to a quadratic kinetic equation. This equation describes the long time behaviour of weak solutions with finite mass to the weak turbulence equation associated to the nonlinear…
We derive a satisfying rate of convergence of the Marcus-Lushnikov process toward the solution to Smoluchowski's coagulation equation. Our result applies to a class of homogeneous-like coagulation kernels with homogeneity degree ranging in…
We consider Smoluchowski's coagulation equation with kernels of homogeneity one of the form $K_{\varepsilon }(\xi,\eta) =\big( \xi^{1-\varepsilon }+\eta^{1-\varepsilon }\big)\big ( \xi\eta\big) ^{\frac{\varepsilon }{2}}$. Heuristically, in…
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…