Related papers: Stability and Optimization in Structured Populatio…
We study the optimization of the stable marriage problem. All individuals attempt to optimize their own satisfaction, subject to mutually conflicting constraints. We find that the stable solutions are generally not the globally best…
The initial boundary value problem for a class of scalar non autonomous conservation laws in one space dimension is proved to be well posed and stable with respect to variations in the flux. Targeting applications to traffic, the regularity…
We study the stability of one-dimensional linear lattice Boltzmann schemes for scalar hyperbolic equations with respect to boundary data. Our approach is based on the original raw algorithm on several unknowns, thereby avoiding the need for…
In this paper we study collective decision making on a multi-population, represented by a regular network of groups of individuals. Each group consists of a collection of players and every player can choose between two options. A group is…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
We analyse the asymptotic behaviour of a nonlinear mathematical model of cellular proliferation which describes the production of blood cells in the bone marrow. This model takes the form of a system of two maturity structured partial…
The study of density-dependent stochastic population processes is important from a historical perspective as well as from the perspective of a number of existing and emerging applications today. In more recent applications of these…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
We present a unified framework ensuring well posedness and providing stability estimates to a class of Initial Boundary Value Problems for renewal equations comprising a variety of biological or epidemiological models. This versatility is…
A novel model of biological organisms is advanced, treating an organism as a self-consistent system subject to a pathogen flux. The principal novelty of the model is that it describes not some parts, but a biological organism as a whole.…
We introduce a spatial economic growth model where space is described as a network of interconnected geographic locations and we study a corresponding finite-dimensional optimal control problem on a graph with state constraints. Economic…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
A system made up of N interacting species is considered. Self-reaction terms are assumed of the logistic type. Pairwise interactions take place among species according to different modalities, thus yielding a complex asymmetric disordered…
We describe the spectra of certain tridiagonal matrices arising from differential equations commonly used for modeling flocking behavior. In particular we consider systems resulting from allowing an arbitrary boundary condition for the end…
The paper investigates stability properties of solutions of optimal control problems for semilinear parabolic partial differential equations. H\"older or Lipschitz dependence of the optimal solution on perturbations are obtained for…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
We prove the stability with respect to the flux of solutions to initial-boundary value problems for scalar non-autonomous conservation laws in one space dimension. Key estimates are obtained through a careful construction of the solutions.
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
We consider a control problem constrained by the unsteady stochastic Stokes equations with nonhomogeneous boundary conditions in connected and bounded domains. In this paper, controls are defined inside the domain as well as on the…
We propose and analyze a nonlinear age-structured multi-species model that serves as a unifying framework for ecological and biotechnological systems in complex environments (microbial communities, bioreactors, and others). The formulation…