English
Related papers

Related papers: Spatial coagulation with bounded coagulation rate

200 papers

In this paper we prove that the time dependent solutions of a large class of Smoluchowski coagulation equations for multicomponent systems concentrate along a particular direction of the space of cluster compositions for long times. The…

Analysis of PDEs · Mathematics 2024-10-02 Marina A. Ferreira , Jani Lukkarinen , Alessia Nota , Juan J. L. Velázquez

An existence result on weak solutions to the continuous coagulation equation with collision-induced multiple fragmentation is established for certain classes of unbounded coagulation, collision and breakup kernels. In this model, a pair of…

Analysis of PDEs · Mathematics 2018-02-27 Prasanta Kumar Barik , Ankik Kumar Giri

Inertial particles suspended in many natural and industrial flows undergo coagulation upon collisions and fragmentation if their size becomes too large or if they experience large shear. Here we study this coagulation-fragmentation process…

Chaotic Dynamics · Physics 2009-08-20 Jens C. Zahnow , Rafael D. Vilela , Ulrike Feudel , Tamás Tél

In this article, the uniqueness of weak solutions to the continuous coagulation and multiple fragmentation equation is proved for a large range of unbounded coagulation and multiple fragmentation kernels. The multiple fragmentation kernels…

Analysis of PDEs · Mathematics 2013-03-26 Ankik Kumar Giri

We study a problem involving thermosolutal convection in a fluid when the solute concentration is subject to a chemical reaction in which the solubility of the dissolved component is a function of temperature. When the spatial domain is a…

Analysis of PDEs · Mathematics 2021-03-19 Michele Ciarletta , Brian Straughan , Vincenzo Tibullo

Existence of mass-conserving weak solutions to the coagulation-fragmentation equation is established when the fragmentation mechanism produces an infinite number of fragments after splitting. The coagulation kernel is assumed to increase at…

Analysis of PDEs · Mathematics 2018-04-25 Philippe Laurençot

We study coagulation equations under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. We consider both discrete and continuous coagulation equations, and allow for a large class of…

Mathematical Physics · Physics 2020-09-28 Marina A. Ferreira , Jani Lukkarinen , Alessia Nota , Juan J. L. Velázquez

We study a spatial Markovian particle system with pairwise coagulation, a spatial version of the Marcus--Lushnikov process: according to a coagulation kernel $K$, particle pairs merge into a single particle, and their masses are united. We…

Probability · Mathematics 2024-01-15 Luisa Andreis , Wolfgang König , Heide Langhammer , Robert I. A. Patterson

We establish spatial a priori estimates for the solution u to a class of dilation invariant Kolmogorov equation, where u is assumed to only have a certain amount of regularity in the diffusion's directions. The result is that u is also…

Analysis of PDEs · Mathematics 2021-10-14 Francesca Anceschi

We are interested in the kernel of one-dimensional diffusion equations with continuous coefficients as evaluated by means of explicit discretization schemes of uniform step $h>0$ in the limit as $h\to0$. We consider both semidiscrete…

Numerical Analysis · Mathematics 2007-11-02 Claudio Albanese

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…

Analysis of PDEs · Mathematics 2019-10-18 José A. Cañizo , Sebastian Throm

Binary coagulation is an important process in aerosol dynamics by which two particles merge to form a larger one. The distribution of particle sizes over time may be described by the so-called Smoluchowski's coagulation equation. This…

Mathematical Physics · Physics 2021-06-25 Marina A. Ferreira

The critical coagulation-fragmentation equation with multiplicative coagulation and constant fragmentation kernels is known to not have global mass-conserving solutions when the initial mass is greater than $1$. We show that for any given…

Analysis of PDEs · Mathematics 2022-12-13 Hung V. Tran , Truong-Son Van

In this article we prove the existence of solutions to the singular coagulation equation with multifragmentation. We use weighted $L^1$-spaces to deal with the singularities and to obtain regular solutions. The Smoluchowski kernel is…

Mathematical Physics · Physics 2013-10-30 Carlos Cueto Camejo , Gerald Warnecke

This article deals with the convergence of finite volume scheme (FVS) for solving coagulation and multiple fragmentation equations having locally bounded coagulation kernel but singularity near the origin due to fragmentation rates. Thanks…

Numerical Analysis · Mathematics 2022-10-04 Sanjiv Kumar Bariwal , Prasanta Kumar Barik , Ankik Kumar Giri , Rajesh Kumar

Well posedness is established for a family of equations modelling particle populations undergoing delocalised coagulation, advection, inflow and outflow in a externally specified velocity field. Very general particle types are allowed while…

Analysis of PDEs · Mathematics 2018-02-08 Robert I. A. Patterson

The aim of this two-part paper is to investigate the stability properties of a special class of solutions to a coagulation-fragmentation equation. We assume that the coagulation kernel is close to the diagonal kernel, and that the…

Analysis of PDEs · Mathematics 2019-06-24 Marco Bonacini , Barbara Niethammer , Juan Velázquez

For a substance diffusing on a curved surface, we obtain an explicit relation valid for very small values of the time, between the local concentration, the diffusion coefficient, the intrinsic spatial curvature and the time. We recover the…

Biological Physics · Physics 2009-11-10 J. Balakrishnan

Quadrature formulas for spheres, the rotation group, and other compact, homogeneous manifolds are important in a number of applications and have been the subject of recent research. The main purpose of this paper is to study coordinate…

Numerical Analysis · Mathematics 2012-11-26 E. Fuselier , T. Hangelbroek , F. J. Narcowich , J. D. Ward , G. B. Wright

In this work, we study a particular system of coagulation equations characterized by two values, namely volume $v$ and surface area $a$. Compared to the standard one-dimensional models, this model incorporates additional information about…

Analysis of PDEs · Mathematics 2024-03-12 Iulia Cristian , Juan J. L. Velázquez