Related papers: Age-dependent equations with non-linear diffusion
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the…
We discuss several models of the dynamics of interacting populations. The models are constructed by nonlinear differential equations and have two sets of parameters: growth rates and coefficients of interaction between populations. We…
In this article we first derive some sufficient conditions to establish the monotonicity and comparison principles of the semi-flow generated by non-densely defined Cauchy problems. We apply our results to a class of age structured…
We consider here a logistic equation, modeling processes of nonlocal character both in the diffusion and proliferation terms. More precisely, for populations that propagate according to a L\'evy process and can reach resources in a…
In order to understand how nonlocal diffusion and pulse intervention affect dynamics of species, we focus on an age-structured nonlocal diffusion model in moving and heterogeneous environment, where nonlocal diffusion describes the long…
Existence of nontrivial nonnegative equilibrium solutions for age structured population models with nonlinear diffusion is investigated. Introducing a parameter measuring the intensity of the fertility, global bifurcation is shown of a…
In this paper the spatial-temporal dynamics of the members of interacting populations is described by nonlinear partial differential equations. We consider the migration as a diffusion process influenced by the changing values of the birth…
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…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
A compartment epidemic model for infectious disease spreading is investigated, where movement of individuals is governed by spatial diffusion. The model includes infection age of the infected individuals and assumes a logistic growth of the…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
We review some results on abstract linear and nonlinear population models with age and spatial structure. The results are mainly based on the assumption of maximal $L_p$-regularity of the spatial dispersion term. In particular, this…
Modeling how individuals evolve over time is a fundamental problem in the natural and social sciences. However, existing datasets are often cross-sectional with each individual observed only once, making it impossible to apply traditional…
The nonexponential relaxation and aging inherent to complex dynamics manifested in a wide variety of dissipative systems is analyzed through a model of diffusion in phase space in the presence of a nonconservative force. The action of this…
We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence,…
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 paper, we investigate an eigenvalue problem associated with an age-structured operator incorporating random diffusion and advection. Our primary focus is on examining the asymptotic behaviors of the principal eigenvalue with respect…
We analyze the effect of nonlinear boundary conditions on an advection-diffusion equation on the half-line. Our model is inspired by models for crystal growth where diffusion models diffusive relaxation of a displacement field, advection is…
Neutral models for the dynamics of a system of competing species are used, nowadays, to describe a wide variety of empirical communities. These models are used in many situations, ranging from population genetics and ecological biodiversity…