On a first‐order hyperbolic coagulation model

Abstract

SUMMARYWe consider a ÿrst-order hyperbolic initial-boundary value problem that models coagulation of particles. We establish a comparison principle and construct monotone sequences to show the existence and uniqueness of the solution.

Phytoplankton Dynamics: from the Behavior of Cells to a Transport Equation

“…Similar equations are used in the completely different context of polymerization/depolymerization of chemical particles (cf. [1,7,9,36,46]). Other results concerning this subject can be found in [4,20,30] and the papers quoted there.…”

Existence-uniqueness and monotone approximation for a phytoplankton-zooplankton aggregation model

“…Our arguments here are in the spirit of those used for a coagulation model [2]. Such arguments are based on a novel definition of coupled upper and lower solutions, the establishment of a comparison principle and the construction of monotone sequences of upper and lower solutions which will lead to the existence of the solution by passing to the limit.…”

“…In recent years, several studies have been devoted to the development of phytoplankton aggregation population models (see [2]- [5] and the references cited therein). In [4] an autonomous size-structured model describing the dynamics of phytoplankton aggregation was investigated.…”

“…A finite difference method approximating the solution was developed and the convergence of this approximation to a unique bounded variation solution was established. In [2] a nonautonomous version of the model discussed in [4] was considered with an unbounded domain for the particle size, and existenceuniqueness results were established via the construction of monotone sequences.…”

Explicit solutions to some fragmentation equations with growth or decay

“…Fragmentation and coagulation processes consisting, in splitting large clusters in smaller blocks and, conversely, forming of larger clusters from smaller ones, are abundant in natural and technological processes. We can mention animal groups formation, [1,2,3], phytoplankton dynamics, [4,5,6], polymer degradation, [7,8,9,10], and many others, see [11].…”