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We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the…
In the present paper we analyze the linear stability of a hierarchical size-structured population model where the vital rates (mortality, fertility and growth rate) depend both on size and a general functional of the population density…
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary…
In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an "active" phase when individuals…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
We consider a size-structured aggregation and growth model of phytoplankton community proposed by Ackleh and Fitzpatrick [2]. The model accounts for basic biological phenomena in phytoplankton community such as growth, gravitational…
In this paper we consider a physiologically structured population model with distributed states at birth, formulated on the space of non-negative Radon measures. Using a characterisation of the pre-dual space of bounded Lipschitz functions,…
Phenotypically structured equations arise in population biology to describe the interaction of species with their environment that brings the nutrients. This interaction usually leads to selection of the fittest individuals. Models used in…
We consider linear age-structured population equations with diffusion. Supposing maximal regularity of the diffusion operator, we characterize the generator and its spectral properties of the associated strongly continuous semigroup. In…
We investigate steady states of a quasilinear first order hyperbolic partial integro-differential equation. The model describes the evolution of a hierarchical structured population with distributed states at birth. Hierarchical…
We consider the well-posedness of a model for a flow-structure interaction. This model describes the dynamics of an elastic flexible plate with clamped boundary conditions immersed in a supersonic flow. A perturbed wave equation describes…
This paper is concerned with the global dynamics of a hybrid parabolic-hyperbolic model describing populations with distinct dispersal and sedentary stages. We first establish the global well-posedness of solutions, prove a comparison…
In this work we consider a size-structured cannibalism model with the model ingredients (fertility, growth, and mortality rate) depending on size (ranging over an infinite domain) and on a general function of the standing population…
In this work first we consider a physiologically structured population model with a distributed recruitment process. That is, our model allows newly recruited individuals to enter the population at all possible individual states, in…
We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive…
We investigate a smoothing property for strongly-continuous operator semigroups, akin to ultracontractivity in parabolic evolution equations. Specifically, we establish the stability of this property under certain relatively bounded…
We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and…
This paper is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work…
In this paper we investigate a structured population model with distributed delay. Our model incorporates two different types of nonlinearities. Specifically we assume that individual growth and mortality are affected by scramble…
We study semi-linear evolutionary problems where the linear part is the generator of a positive $C_0$-semigroup. The non-linear part is assumed to be quasi-increasing. Given an initial value in between a sub- and a super-solution of the…