Journal ArticleDOI
Large time behavior in a nonlinear age-dependent population dynamics problem with spatial diffusion.
TLDR
This work analyzes the large time behavior in a nonlinear model of population dynamics with age-dependence and spatial diffusion and shows that when t→+∞ either the solution of the problem goes to 0 or it stabilizes to a nontrivial stationary solution.Abstract:
In this work we analyze the large time behavior in a nonlinear model of population dynamics with age-dependence and spatial diffusion. We show that when t→+∞ either the solution of our problem goes to 0 or it stabilizes to a nontrivial stationary solution. We give two typical examples where the stationary solutions can be evaluated upon solving very simple partial differential equations. As a by-product of the extinction case we find a necessary condition for a nontrivial periodic solution to exist. Numerical computations not described below show a rapid stabilization.read more
Citations
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Book ChapterDOI
Population Models Structured by Age, Size, and Spatial Position
TL;DR: In this paper, the authors use the theory of semigroups of linear and nonlinear operators in Banach spaces to analyze population models incorporating age, size, and spatial structure.
Journal Article
On integrated semigroups and age structured models in {$L^p$} spaces
Pierre Magal,Shigui Ruan +1 more
TL;DR: In this article, the authors considered the non-homogeneous Cauchy problem and proved necessary and sufficient conditions for the existence of mild solutions for non-densely defined nonhomogeneous problems.
Journal ArticleDOI
Age-structured population models and their numerical solution
TL;DR: In this paper, the authors consider the state of the art of the numerical solution of age-structured population models and review the stability and convergence results for different numerical approaches to this kind of problems.
Journal ArticleDOI
Computational Methods and Results for Structured Multiscale Models of Tumor Invasion
TL;DR: This work presents multiscale models of cancer tumor invasion with components at the molecular, cellular, and tissue levels, and provides biological justifications for the model components.
References
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Book
Linear and Quasilinear Equations of Parabolic Type
TL;DR: In this article, the authors considered a hyperbolic parabolic singular perturbation problem for a quasilinear equation of kirchhoff type and obtained parameter dependent time decay estimates of the difference between the solutions of the solution of a quasi-linear parabolic equation and the corresponding linear parabolic equations.
Journal ArticleDOI
On the Existence of Positive Solutions of Semilinear Elliptic Equations
TL;DR: In this article, the existence of positive solutions of semilinear elliptic equations is studied and the results are also interpreted in terms of bifurcation diagrams, and in each case nearly optimal multiplicity results are obtained.
Journal ArticleDOI
Non-linear age-dependent population dynamics
TL;DR: In this paper, the Malthusian law is shown to be inapplicable to situations in which the population competes for resources (e.g., space and food), for in these situations 5 should depend on the size of the population.
MonographDOI
Mathematical theories of populations : demographics, genetics and epidemics
TL;DR: The Equations of Population Dynamics: Age Dependent Population Growth Analysis of the Birth Rate A Model of a Self-Limiting Population A Two-sex Model Deterministic Models in Genetics: A Brief Introduction to Mendelian Genetics as discussed by the authors.