Related papers: A Distributional Solution to a Hyperbolic Problem …
This paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by [17]. Moreover, its multiplicative structure and the multiplicative…
We study the inverse problems for the second order hyperbolic equations of general form with time-dependent coefficients assuming that the boundary data are given on a part of the boundary. The main result of this paper is the determination…
The paper was suggested by a brief note of the second author about the application of the Hubbert curve to predict decay of resource exploitation. A further suggestion came from the interpretation of the Hubbert curve in terms of a specific…
The time evolution of spatial fluctuations in inhomogeneous d-dimensional biological systems is analyzed. A single species continuous growth model, in which the population disperses via diffusion and convection is considered.…
The Luria-Delbr\"uck mutation model has a long history and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using some mathematical tools from nonlinear…
This work outlines a time-domain numerical integration technique for linear hyperbolic partial differential equations sourced by distributions (Dirac $\delta$-functions and their derivatives). Such problems arise when studying binary black…
A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of the distribution function. Assuming enough initial moments…
The population dynamics that evolves in the radial symmetric geometry is investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate…
The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the Dirac equation is developed. Avoiding disadvantages of the standard approach in the description of exited…
We review a little-known treatment of the relativistic two-body bound-state problem - that provided by Two-Body Dirac Equations obtained from constraint dynamics. We describe some of its more important results, its relation to older…
We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum…
This paper analyzes a stochastic logistic difference equation under the assumption that the population distribution follows a normal distribution. Our focus is on the mathematical relationship between the average growth rate and a newly…
We study quantitative large-time averages for Hamilton--Jacobi equations in a dynamic random environment that is stationary ergodic and has unit-range dependence in time. Our motivation comes from stochastic growth models related to the…
In this article we consider regularizations of the Dirac delta distribution with applications to prototypical elliptic and hyperbolic partial differential equations (PDEs). We study the convergence of a sequence of distributions…
The main purpose of this paper is to study the existence of periodic solutions for a nonautonomous differential-difference system describing the dynamics of hematopoietic stem cell (HSC) population under some external periodic regulatory…
We study the asymptotic behavior of an integro-dierential equation describing the evolutionary adaptation of a population structured by a phenotypic trait. The model takes into account mutation, selection, horizontal gene transfer and…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
We construct a pathwise formulation for a multi-type age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational…
This work is devoted to the study of scaling limits in small mutations and large time of the solutions u^$\epsilon$ of two deterministic models of phenotypic adaptation, where the parameter $\epsilon$ > 0 scales the size of mutations. The…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…