1,721,019 research outputs found
Confinement strategies in a model for the interaction between individuals and a continuum
No full textThis paper presents the basic analytical theory for a model that describes interactions between a few individuals (or agents) and a population (a continuum), all moving in R n. The agents affect the population, either repelling or attracting it. Their aim is to steer the population toward a given region K ⊂ R n. This can be seen as a control problem where the state of the system is the set occupied by the population. In this paper we solve simple confinement problems, where the agents' task is to keep the population within a given set. Rigorous analytical results as well as numerical computations are presented. © 2012 Society for Industrial and Applied Mathematics
Well-posedness and control in a hyperbolic–parabolic parasitoid–parasite system
Full text linkWe develop a time and space-dependent predator—prey model. The predators' equation is a nonlocal hyperbolic balance law, while the diffusion of prey obeys a parabolic equation, so that predators “hunt” for prey, while prey diffuse. A control term allows to describe the use of predators as parasitoids to limit the growth of prey–parasites. The general well-posedness and stability results here obtained ensure the existence of optimal pest control strategies, as discussed through some numerical integrations. The specific example we have in mind is that of Trichopria drosophilæ used to fight against the spreading of Drosophila suzukii
NON LINEAR HYPERBOLIC-PARABOLIC SYSTEMS WITH DIRICHLET BOUNDARY CONDITIONS
Full text linkWe prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on data and parameters are also provided. These equations appear in models devoted to population dynamics or to epidemiology, for instance
Well Posedness and Control in a NonLocal SIR Model
No full textSIR models, also with age structure, can be used to describe the evolution of an infectious disease. A vaccination campaign influences this dynamics immunizing part of the susceptible individuals, essentially turning them into recovered individuals. We assume that vaccinations are dosed at prescribed times or ages which introduce discontinuities in the evolution of the S and R populations. It is then natural to seek the “best” vaccination strategies in terms of costs and/or effectiveness. This paper provides the basic well posedness and stability results on the SIR model with vaccination campaigns, thus ensuring the existence of optimal dosing strategies
On the control of moving sets: Positive and negative confinement results
No full textWe consider a few individuals whose task is to confine a moving population. This is a control problem where the state to be controlled is a compact subset of Rn. We first prove a negative result on the impossibility of confinement, a key assumption being a sufficiently large initial volume. Then a positive result is also provided through the construction of a confining control, when the initial set has a suitable diameter. Numerical integrations show possible behaviors when the above results do not apply. © 2013 Society for Industrial and Applied Mathematics
Balance Laws with Singular Source Term and Applications to Fluid Dynamics
No full textConsider a balance law where the flux may depend explicitly on the space variable. At jump discontinuities, modeling considerations may impose the defect in the conservation of some quantities, thus leading to non conservative products. Below, we deduce the evolution in the smooth case from the jump conditions at discontinuities. Moreover, the resulting framework enjoys well posedness and solutions are uniquely characterized. These results apply, for instance, to the flow of water in a canal with varying width and depth, as well as to the inviscid Euler equations in pipes with varying geometry
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