Espaces non verifiant le second axiome de denombrabilité.
We extend some known sigma-finiteness and regularity results for (locally finite) Radon measures to locally sigma-finite or locally moderated Radon measures of type (H), and we obtain other new ones. The main result states that the regularity and the sigma-finiteness are equivalent for alllocally moderated, diffused, Radon measures of type (H) in a T1 topological space which is either weakly metacompact or paralindelöf (resp. metalindelöf) and has a concassage of Lindelöf (resp. separable) subsets....
We consider a time optimal control problem arisen from the optimal management of a bioreactor devoted to the treatment of eutrophicated water. We formulate this realistic problem as a state-control constrained time optimal control problem. After analyzing the state system (a complex system of coupled partial differential equations with non-smooth coefficients for advection-diffusion-reaction with Michaelis-Menten kinetics, modelling the eutrophication processes) we demonstrate the existence of,...
In this paper we study the role that unimodular functions play in deciding the uniform boundedness of sets of continuous linear functionals on various function spaces. For instance, inner functions are a UBD-set in H with the weak-star topology.
We consider a time optimal control problem arisen from the optimal management of a bioreactor devoted to the treatment of eutrophicated water. We formulate this realistic problem as a state-control constrained time optimal control problem. After analyzing the state system (a complex system of coupled partial differential equations with non-smooth coefficients for advection-diffusion-reaction with Michaelis-Menten kinetics, modelling the eutrophication processes) we demonstrate the existence of,...
In this paper, a dynamic viscoelastic problem is numerically studied. The variational problem is written in terms of the velocity field and it leads to a parabolic linear variational equation. A fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize time derivatives. An error estimates result is recalled, from which the linear convergence is derived under suitable regularity conditions. Then, an error analysis...
In this paper, a dynamic viscoelastic problem is numerically studied. The variational problem is written in terms of the velocity field and it leads to a parabolic linear variational equation. A fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize time derivatives. An error estimates result is recalled, from which the linear convergence is derived under suitable regularity conditions. Then, an error analysis...
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