Mathematical Models and Methods in Applied Sciences

The stationary Stokes equations of a viscous incompressible fluid are considered in domains Ω with m > 1 outlets to infinity, which have in some coordinate system the following form

We study the membrane-dominated deformation state of a thin shell, the midsurface of which is located on a hyperbolic surface of revolution whose boundary is a curvilinear polygon. The shell is loaded by a surface tractions on both faces, and clamped all along the edge. Proceeding from the classical shell model of Koiter–Sanders–Novozhilov, an asymptotic membrane theory model is constructed to describe the limit behavior of the shell as the thickness tends to zero. The mathematical properties of the membrane theory are analyzed and the convergence rate estimate between the two models is proven.

In this paper a mathematical framework of the control theory of manufacturing systems is proposed. All possible plant structures are classified. A mathematical dynamical model which describes the dynamics of a plant is developed. With the help of this model it is shown how the real time control policy which guarantees the stable work of the plant with the quasi-maximal production rate can be designed.

The aim of this paper is to give a method which permits us to describe how individual properties can emerge at the population level, in population dynamics. We consider interacting populations. In order to take into account the spatial or behavioral heterogeneity, we subdivide each population into subpopulations. A given subpopulation corresponds to those individuals having the same behavior and who are in a homogeneous environment. Furthermore, we assume that the migration process is faster than the growth and interaction processes. Therefore, we must study models with many variables coupled together into large scaled differential systems. Firstly, our method permits us to reduce these complex systems into simpler ones, which will be called reduced systems. Secondly, these reduced systems give the population dynamics and contains informations about individuals' behavior, that is we can explain how individual dynamics emerge in the population dynamics. We already investigated the case where the fast dynamics reach an equilibrium in previous works. In this paper, we are interested in those models where the fast dynamics oscillates because it is ecologically relevant.

We study the asymptotic behavior of a viscous, barotropic and compressible fluid in a porous medium Ω_ε, (ε > 0) obtained by removing from an open set Ω some small obstacles with size a_ε ≪ ε. We establish that the fluid behaves differently depending on whether the size a_ε is greater than or smaller than a critical size c_ε. If it is greater than or equal to c_ε a convolution term appears in the limit problem. This corresponds to a long memory effect. On the contrary, if the size is smaller than c_ε, the fluid behaves as if there is no obstacle.

Modeling and analysis of models of complex chemical reactions constitute wide branches of research in chemistry, physics and mathematics. Here a model is proposed which is amenable to rigorous mathematical study, which makes clear the dynamics of the systems described by such a model. In particular, only combinations of chemical reactions which preserve the number of particles, and which have equal forward and backward reaction rates are allowed. Reactions which do not satisfy such requirements can be considered, provided they are suitably modified. Also, it is required that the densities of the chemicals in the reactions be low, so that the applicability of the theory is restricted to mixtures of gases.

A fixed point argument is used to prove the existence and uniqueness of solutions for the unsteady deep Bénard convection equations in for .

We introduce a model of transport of particles in a network, which is represented by a connected graph with m vertices and n edges. Each edge represents a one-dimensional conductor of particles, whose behavior is described by means of a linear Boltzmann-like equation. In graph vertices, a system of linear boundary conditions is given which takes into account the exchanges of particles between the edges. The well-posedness of the initial value problem is studied into an abstract L¹-like setting and the structure of the solution is given for simplest case of pure streaming transport.