Measure-valued solutions for a hierarchically size-structured population

Finite difference approximations for measure-valued solutions of a hierarchically size-structured population model.

We study a quasilinear hierarchically size-structured population model presented in [4]. In this model the growth, mortality and reproduction rates are assumed to depend on a function of the population density. In [4] we showed that solutions to this model can become singular (measure-valued) in finite time even if all the individual parameters are smooth. Therefore, in this paper we develop a ...

Weak Solutions and Differentiability for Size - Structured Population Models

On periodic cohort solutions of a size-structured population model

We consider a size-structured population model with discontinuous reproduction and feedback through the environmental variable \substrate". The model admits solutions with nitely many cohorts and in that case the problem is described by a system of ODEs involving a bifurcation parameter. Existence of nontrivial periodic n-cohort solutions is investigated. Moreover, we discuss the question wheth...

Weak-strong Uniqueness for Measure-valued Solutions

We prove the weak-strong uniqueness for measure-valued solutions of the incompressible Euler equations. These were introduced by R.DiPerna and A.Majda in their landmark paper [10], where in particular global existence to any L initial data was proven. Whether measure-valued solutions agree with classical solutions if the latter exist has apparently remained open. We also show that DiPerna’s mea...

Particle Representations for Measure - Valued Population Models

Models of populations in which a type or location, represented by a point in a metric space E, is associated with each individual in the population are considered. A population process is neutral if the chances of an individual replicating or dying do not depend on its type. Measurevalued processes are obtained as infinite population limits for a large class of neutral population models, and it...