相关论文: Stabilization of Age-Structured Chemostat Hyperbol…

This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…

The superior Fisher-Kopeliovich closure is applied to the hierarchy of master equations for spatial moments of population dynamics for the first time. As a consequence, the population density, pair and triplet distribution functions are…

We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behaviour…

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…

In many biological systems, natural selection acts simultaneously on multiple levels of organization. This scenario typically presents an evolutionary conflict between the incentive of individuals to cheat and the collective incentive to…

First-order systems of hyperbolic partial differential equations (PDEs) occur ubiquitously throughout computational physics, commonly used in simulations of fluid turbulence, shock waves, electromagnetic interactions, and even general…

We study interacting particle systems driven by noise, modeling phenomena such as opinion dynamics. We are interested in systems that exhibit phase transitions i.e. non-uniqueness of stationary states for the corresponding McKean-Vlasov…

Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…

We consider an interlinked production model consisting of conservation laws (PDE) coupled to ordinary differential equations (ODE). Our focus is the analysis of control laws for the coupled system and corresponding stabilization questions…

We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a "sizer-timer"…

A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed…

We investigate the hydrodynamic stability and the formation of patterns in a continuum model of epithelial layers, able to account for the interplay between mechanical activity, lateral adhesion and the $6-$fold orientational order…

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…

In this paper, we design a controller for an interconnected system composed of a linear Stochastic Differential Equation (SDE) controlled through a linear hetero-directional hyperbolic Partial Differential Equation (PDE). Our objective is…

We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…

Inspired by the works of Hughes [17, 18], we formalize and prove the well posedness of a hyperbolic--elliptic system whose solutions describe the dynamics of a moving crowd. The resulting model is here shown to be well posed and the time of…

Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…

There has been renewed interest in understanding the mathematical structure of ecological population models that lead to overcompensation, the process by which a population recovers to a higher level after suffering a permanent increase in…

We consider population models in which the individuals reproduce, die and also migrate in space. The population size scales according to some parameter $N$, which can have different interpretations depending on the context. Each individual…

This paper is concerned with the output feedback boundary stabilization of general 1-D reaction diffusion PDEs in the presence of an arbitrarily large input delay. We consider the cases of Dirichlet/Neumann/Robin boundary conditions for the…