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791
Motivated by a mathematical model of an age structured proliferating cell population, we state some new variants of Leray-Schauder type fixed point theorems for (ws)-compact operators. Further, we apply our results to establish some new existence and locality principles for nonlinear boundary value problem arising in the theory of growing cell population in L 1-setting. Besides, a topological structure of the set of solutions is provided.
In this paper we consider a nonlinear model of a biological wastewater treatment process, based on two microbial populations and two substrates. The model, described by a four-dimensional dynamic system, is known to be practically verified and reliable. First we study the equilibrium points of the open-loop system, their stability and local bifurcations with respect to the control variable. Further we propose a feedback control law for asymptotic stabilization of the closed-loop system towards a...
In this paper we study a linear population dynamics model. In this model, the birth process is described by a nonlocal term and the initial distribution is unknown. The aim of this paper is to use a controllability result of the adjoint system for the computation of the density of individuals at some time .
We are concerned with the null controllability of a linear coupled population dynamics system or the so-called prey-predator model with Holling type I functional response of predator wherein both equations are structured in age and space. It is worth mentioning that in our case, the space variable is viewed as the “gene type” of population. The studied system is with two different dispersion coefficients which depend on the gene type variable and degenerate in the boundary. This system will be governed...
We present results on the estimation of unknown parameters in systems of ordinary differential equations in order to fit the output of models to real data. The numerical method is based on the nonlinear least squares problem along with the solution of sensitivity equations corresponding to the differential equations. We will present the performance of the method on the problem of fitting the output of basic compartmental epidemic models to data from the Covid-19 epidemic. This allows us to draw...
This work is concerned with the numerical solution of a hydrodynamic model of the macroscopic behavior of flocks of birds due to Fornasier et al., 2011. The model consists of the compressible Euler equations with an added nonlocal, nonlinear right-hand side. As noticed by the authors of the model, explicit time schemes are practically useless even on very coarse grids in 1D due to the nonlocal nature of the equations. To this end, we apply a semi-implicit discontinuous Galerkin method to solve the...
A three dimensional predator-prey-resource model is proposed and analyzed to study the dynamics of the system with resource-dependent yields of the organisms. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the organisms associated with the system cannot thrive even in the absence of predation. Local stability of the system is obtained in the absence of one or more of the predators and in the presence of all the predators. Under appropriate...
We consider a phase field system based on the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Dirichlet boundary conditions. In particular, we prove, in one and two space dimensions, the existence of a solution which is strictly separated from the singularities of the nonlinear term and that the problem possesses a finite-dimensional global attractor in terms of exponential attractors.
We study existence, uniqueness and form of solutions to the equation where α, β, γ and f are given, and stands for the even part of a searched-for differentiable function g. This equation emerged naturally as a result of the analysis of the distribution of a certain random process modelling a population genetics phenomenon.
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