Related papers: Mass-conserving solutions to coagulation-fragmenta…
We investigate a coagulation-fragmentation equation with boundary data, establishing the well-posedness of the initial value problem when the coagulation kernels are bounded at zero and showing existence of solutions for the singular…
We take into account a coagulation model that simulates a distinct kind of dynamics. In this model, two particles collide to produce a single particle, but the resulting particle decreases in size, allowing each particle to be fully…
We consider the exchangeable fragmentation-coagulation (EFC) processes, where the coagulations are multiple and not simultaneous, as in a $\Lambda$-coalescent, and the fragmentations dislocate at finite rate an individual block into…
The well-posedness of the growth-coagulation equation is established for coagulation kernels having singularity near the origin and growing atmost linearly at infinity. The existence of weak solutions is shown by means of the method of the…
We study infinite systems of particles which undergo coalescence and fragmentation, in a manner determined solely by their masses. A pair of particles having masses $x$ and $y$ coalesces at a given rate $K(x,y)$. A particle of mass $x$…
We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
We study the fragment size distributions after crushing of single and many particles under uniaxial compression inside a cylindrical container by means of numerical simulations. Under the assumption that breaking goes through the bulk of…
The discrete collisional breakage equation, which captures the dynamics of cluster growth when clusters encounter binary collisions with possible matter transfer, is discussed in this article. The existence of global mass-conserving…
The dynamics of the fragmentation equation with size diffusion is investigated when the size ranges in (0, $\infty$). The associated linear operator involves three terms and can be seen as a nonlocal perturbation of a Schr{\"o}dinger…
We prove the existence of weak solutions for distribution-dependent stochastic Volterra equations under linear growth and continuity conditions on the coefficients and mild regularity assumptions on the kernels, including singular kernels.…
In this paper, we consider a continuous fragmentation--coagulation model in which the reacting particles can be transported in physical space through either advection or diffusion. We prove new results on the generation of $C_0$-semigroups…
A discrete version of the nonlinear collision-induced breakage equation is studied. Existence of solutions is investigated for a broad class of unbounded collision kernels and daughter distribution functions, the collision kernel $a_{i,j}$…
Abridged. A large fraction of stars are found in binary systems. It is therefore important for our understanding of the star formation process, to investigate the fragmentation of dense molecular cores. We study the influence of the…
We present a new a-priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this…
Motivated by the occurrence of "shattering" mass-loss observed in purely continuous fragmentation models, this work concerns the development and the mathematical analysis of a new class of hybrid discrete--continuous fragmentation models.…
Inertial particles advected in chaotic flows often accumulate in strange attractors. While moving in these fractal sets they usually approach each other and collide. Here we consider inertial particles aggregating upon collision. The new…
We establish an existence result for weak solutions to an aggregation-diffusion-reaction equation with a constraint, arising in the modelling of multiple sclerosis. The model is derived from a general chemotaxis-type framework and describes…
We investigate the kinetics of nonlinear collision-induced fragmentation. We obtain the fragment mass distribution analytically by utilizing its travelling wave behavior. The system undergoes a shattering transition in which a finite…
We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant…