Related papers: Mass-conserving solutions to coagulation-fragmenta…
The main focus of this work is the asymptotic behavior of mass-conservative homogeneous fragmentations. Considering the logarithm of masses makes the situation reminiscent of branching random walks. The standard approach is to study {\bf…
Persistence problems in weighted spaces have been studied for different dispersive models involving non-local operators. Generally, these models do not propagate polynomial weights of arbitrary magnitude, and the maximum decay rate is…
The existence of weak solutions is established for stochastic Volterra equations with time-inhomogeneous coefficients allowing for general kernels in the drift and convolutional or bounded kernels in the diffusion term. The presented…
In this paper, we study the global conservative weak solutions for a class of nonlinear dispersive wave equations after wave breaking. We first transform the equations into an equivalent semi-linear system by introducing new variables. We…
We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…
We consider a model of fragmentation of sheet by cracks that move with a velocity in preferred direction, but undergo random transverse displacements as they move. There is a non-zero probability of crack-splitting, and the split cracks…
The multifragmentation of excited spherical nuclear sources with various N/Z ratios and fixed mass number is studied within dynamical and statistical models. The dynamical model treats the multifragmentation process as a final stage of the…
First we establish explosion criteria for jump processes with an arbitrary locally compact separable metric state space. Then these results are applied to two stochastic coagulation-fragmentation models--the direct simulation model and the…
This paper concerns the asymptotic behaviour of solutions of a linear convolution Volterra summation equation with an unbounded forcing term. In particular, we suppose the kernel is summable and ascribe growth bounds to the exogenous…
We present a parameter survey of fragmentation in collapsar disks, using a revised version of the Chen & Beloborodov (2007) model that determines the structure of steady state hyperaccretion disks in a general relativistic and neutrino…
Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and…
Global existence of very weak solutions to a non-local diffusion-advection-reaction equation is established under no-flux boundary conditions in higher dimensions. The equation features degenerate myopic diffusion and nonlocal adhesion and…
In this article, we discuss the continuous version of the generalized exchange-driven growth model which is a variant of the coagulation model in which a smaller size particle is detached from a bigger one and merges with another particle.…
A statistical model of fragmentation of aggregates is proposed, based on the stochastic propagation of cracks through the body. The propagation rules are formulated on a lattice and mimic two important features of the process -- a crack…
Dust grains play a significant role in several astrophysical processes, including gas/dust dynamics, chemical reactions, and radiative transfer. Replenishment of small-grain populations is mainly governed by fragmentation during pair-wise…
We present results from a numerical study of critical gravitational collapse of axisymmetric distributions of massless scalar field energy. We find threshold behavior that can be described by the spherically symmetric critical solution with…
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 $\alpha>0$.
Fragmentation and growth-fragmentation equations is a family of problems with varied and wide applications. This paper is devoted to description of the long time time asymptotics of two critical cases of these equations, when the division…