Related papers: Mass-conserving solutions to coagulation-fragmenta…
An explicit solution for a growth fragmentation equation with constant dislocation measure is obtained. In this example the necessary condition for the general results in \cite{BW} about the existence of global solutions in the so called…
In this note, we derive a stability and weak-strong uniqueness principle for volume-preserving mean curvature flow. The proof is based on a new notion of volume-preserving gradient flow calibrations, which is a natural extension of the…
Fragmentation--coagulation processes, in which aggregates can break up or get together, often occur together with decay processes in which the components can be removed from the aggregates by a chemical reaction, evaporation, dissolution,…
We study existence and uniqueness of bounded solutions to a fractional sublinear elliptic equation with a variable coefficient, in the whole space. Existence is investigated in connection to a certain fractional linear equation, whereas the…
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…
In this paper we examine the evolution of solutions, that initially have compact support, of a recently-derived system of cross-coupled Camassa-Holm equations. The analytical methods which we employ provide a full picture for the…
Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. We consider moments of arbitrary orders of the mass multiplicity spectrum and derive scaling properties pertaining to their time…
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
We consider a mass-conserving bistable equation with a saturating flux on an interval. This is the quasilinear analogue of the Rubinstein-Steinberg equation, suitable for description of order parameter conserving solid-solid phase…
A large class of first order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating function is constructed. The conserved…
In the paper, we study spatially distributed particle systems whose time evolution is governed by vanishing diffusion in space $\mathbb{R}^d$, $d\ge 1$, and by size-continuous fragmentation and coagulation processes with unbounded rates. We…
We study an inverse design problem for the linear multiple fragmentation equation arising in particle dynamics. Our objective is to reconstruct an unknown initial size distribution that evolves, under a prescribed fragmentation law, into a…
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…
Existence of stationary solutions to the coagulation-fragmentation equation is shown when the coagulation kernel $K$ and the overall fragmentation rate $a$ are given by $K(x, y) = x^\alpha y^\beta + x^\beta y^\alpha$ and $a(x) = x^\gamma$,…
In this paper we prove the global in time solvability of the continuous growth--fragmentation--coagulation equation with unbounded coagulation kernels, in spaces of functions having finite moments of sufficiently high order. The main tool…
The current paper is concerned with pointwise persistence in full chemotaxis models with local as well as nonlocal time and space dependent logistic source in bounded domains. We first prove the global existence and boundedness of…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
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…
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…
In this paper we discuss some aspects of fragmented condensation from a mathematical perspective. We first propose a simple way of characterizing finite fragmentation. Then, inspired by recent results of semiclassical analysis applied to…