Related papers: Some Remarks About the Semigroup Associated to Age…
This paper is dedicated to the study of the semilinear fractional diffusion-wave equation. We provide estimates on the families of linear operators related to the problem in the fractional power scale associated with the Laplace operator.…
We introduce an age-structured asexual population model containing all the relevant features of evolutionary ageing theories. Beneficial as well as deleterious mutations, heredity and arbitrary fecundity are present and managed by natural…
In this paper we study the preservation of strong stability of strongly continuous semigroups on Hilbert spaces. In particular, we study a situation where the generator of the semigroup has a finite number of spectral points on the…
We provide a growth bound for the operator norm of $C_0$-semigroups on Hilbert spaces under a corresponding growth bound on the resolvent of the semigroup generator. For some super-linear resolvent growths, our estimate is sharper than the…
In this paper, we propose new semiparametric procedures for making inference on linear functionals and their functions of two semicontinuous populations. The distribution of each population is usually characterized by a mixture of a…
We corroborate the idea of a close connection between replica symmetry breaking and aging in the linear response function for a large class of finite-dimensional systems with short-range interactions. In these system, characterized by a…
The spread of a particular trait in a cell population often is modelled by an appropriate system of ordinary differential equations describing how the sizes of subpopulations of the cells with the same genome change in time. On the other…
It is folklore that a power bounded operator on a sequentially complete locally convex space generates a uniformly continuous $C_0$-semigroup which is given by the corresponding power series representation. Recently, Doma\'nski asked if in…
The aim of this paper is twofold: (1) On the one hand, the paper revisits the spectral analysis of semigroups in a general Banach space setting. It presents some new and more general versions, and provides comprehensible proofs, of…
We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the generation of a contraction semigroup, study the relation between the spectra of…
We report new results about the two-time dynamics of an anomalously diffusing classical particle, as described by the generalized Langevin equation with a frequency-dependent noise and the associated friction. The noise is defined by its…
We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with…
Consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources distribution in a given box. We…
We construct normed spaces of real-valued functions with controlled growth on possibly infinite-dimensional state spaces such that semigroups of positive, bounded operators $(P_t)_{t\ge 0}$ thereon with $\lim_{t\to 0+}P_t f(x)=f(x)$ are in…
We show that for a family of problems described by non-linear diffusion equations an exact calculation of the two time correlation function gives C(t,t')=f(t-t')g(t'), t>t', exhibiting normal and anomalous diffusions, as well as aging…
We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an…
This paper deals with some control problems related to structured population dynamics with diffusion. Firstly, we investigate the regional control for an optimal harvesting problem (the control acts in a subregion $\omega$ of the whole…
I consider ageing behaviour in two exactly solvable reaction-diffusion systems. Ageing exponents and scaling functions are determined. I discuss in particular a case in which the equality of two critical exponents, known from systems with…
It is proved that the numerical semigroups associated to the combinatorial configurations satisfy a family of non-linear symmetric patterns. Also, these numerical semigroups are studied for two particular classes of combinatorial…
The asymptotic stability of the null equilibrium of a linear population model with two physiological structures formulated as a first-order hyperbolic PDE is determined by the spectrum of its infinitesimal generator. We propose an…