Related papers: Existence of the global solutions of an integro-di…
We consider the discrete-time migration-recombination equation, a deterministic, nonlinear dynamical system that describes the evolution of the genetic type distribution of a population evolving under migration and recombination in a law of…
A time-space fractional reaction-diffusion equation in a bounded domain is considered. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time. However, for realistic initial conditions,…
In this paper we study one dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. We establish global existence-uniqueness of classical solutions assuming that the…
In this paper, we study the initial value problem for infinite dimensional fractional non-autonomous reaction-diffusion equations. Applying general time-splitting methods, we prove the existence of solutions globally defined in time using…
Nowadays, in our globalized world,the local and intercountry movements of population have been increased. This situation makes it important for host countries to do right predictions for the future population of their native people as well…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
We consider a class of evolution equations describing population dynamics in the presence of a carrying capacity depending on the population with delay. In an earlier work, we presented an exhaustive classification of the logistic equation…
This paper provides results on local and global existence for a class of solutions to the Euler equations for an incompressible, inviscid fluid. By considering a class of solutions which exhibits a characteristic growth at infinity we…
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is…
In this paper, we study the global existence and regularity of H\"older continuous solutions for a series of nonlinear partial differential equations describing nonlinear waves.
In this paper we prove a theorem of global time-extension for the local classical solution of Navier-Stokes's evolution problem in $\Real^n$ with $n\geqslant2$ for incompressible fluids subjected to external forces and regular initial…
We consider a class of nonlocal reaction-diffusion problems, referred to as replicator-mutator equations in evolutionary genetics. By using explicit changes of unknown function, we show that they are equivalent to the heat equation and,…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence, uniqueness and path-continuity of infinite-time solutions is proved by an extension of the Ovsyannikov method. This…
In this research, we would like to study the global (in time) existence of small data solutions to the following damped $\sigma$-evolution equations with nonlocal (in space) nonlinearity: \begin{equation*}…
We consider an initial value problem for a nonlocal differential equation with a bistable nonlinearity in several space dimensions. The equation is an ordinary differential equation with respect to the time variable t, while the nonlocal…
A new approach is used to describe the large time behavior of the non-local differential equation initially studied in [3]. Our approach is based upon the existence of infinitely many Lyapunov functionals and allows us to extend the…
In the paper, we study spatially distributed particle systems whose time evolution is governed by vanishing diffusion in space $\mathbb{R}^d$, $d\ge 1$, and by size-continuous fragmentation and coagulation processes with unbounded rates. We…
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…
This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained…
The generalization of the simplest equation method to look for exact solutions of systems of nonlinear differential equations is presented. The exact solutions of NDE systems describing the evolution of two interacting populations in two…