Singular perturbations of some nonlinear problems

We deal with singular perturbations of nonlinear problems depending on a small parameter ε > 0. First we consider the abstract theory of singular perturbations of variational inequalities involving some nonlinear operators, defined in Banach spaces, and describe the asymptotic behavior of these solutions as ε → 0. Then these abstract results are applied to some boundary value problems. Bibliography: 15 title

Correctors for some asymptotic problems

In the theory of anisotropic singular perturbation boundary value problems, the solution u ɛ does not converge, in the H 1-norm on the whole domain, towards some u 0. In this paper we construct correctors to have good approximations of u ɛ in the H 1-norm on the whole domain. Since the anisotropic singular perturbation problems can be connected to the study of the asymptotic behaviour of problems defined in cylindrical domains becoming unbounded in some directions, we transpose our results for such problems

Exponential stability of the wave equation with memory and time delay

We study the asymptotic behaviour of the wave equation with viscoelastic damping in presence of a time-delayed damping. We prove exponential stability if the amplitude of the time delay term is small enough

Comparison between three-dimensional linear and nonlinear tsunami generation models

The modeling of tsunami generation is an essential phase in understanding tsunamis. For tsunamis generated by underwater earthquakes, it involves the modeling of the sea bottom motion as well as the resulting motion of the water above it. A comparison between various models for three-dimensional water motion, ranging from linear theory to fully nonlinear theory, is performed. It is found that for most events the linear theory is sufficient. However, in some cases, more sophisticated theories are needed. Moreover, it is shown that the passive approach in which the seafloor deformation is simply translated to the ocean surface is not always equivalent to the active approach in which the bottom motion is taken into account, even if the deformation is supposed to be instantaneous.Comment: 39 pages, 16 figures; Accepted to Theoretical and Computational Fluid Dynamics. Several references have been adde

Optegnelser af presten Oluf Bentsen Mandal for aarene 1625-36.

Anthropogenic radionuclide inputs in the Loire estuary (French Atlantic coast) consist of radioactive releases from 14 nuclear reactors located along the Loire river basin, and of fallout from nuclear weapon tests and from the Tchernobyl accident. To estimate to what extent radionuclides associated with sediment accumulate in the estuary, three complementary approaches were used: field surveys, laboratory experiments and numerical modelling. Sampling of bottom sediments, water and suspended solids was carried out at 8 different dates over a 15 month-period. Analysis covered 14C, 90Sr, 3H, the naturally occurring gamma-emitters (uranium and thorium decay chains, 7Be and 40K), and the artificial gamma emitters (mainly cobalt and cesium isotopes). To gain information on the contamination history of the estuary, sediment cores were also collected at different locations inside and outside the estuarine zone. Processes of radionuclide transport and exchange between dissolved and particulate phases were included in a previously developed estuary specific 2D-hydrodynamic model. Equations of sorption and desorption kinetics were derived from laboratory experiments conducted at different salinities. Simulations carried out for two river discharge conditions (low summer flow, high winter flow) allowed to follow radionuclide desorption in the estuary. For long term simulations, a simplified model was developed. It provided estimates of the amount of radionuclides expelled out of the estuary under dissolved and particulate forms, of the transit time for both forms and of the variations in radionuclides concentrations in the fluid mud. Based on computed results and observations, contributions from different origins (natural, military, industrial, marine, continental) to the inventory of radioactivity in the estuary are presented

On the asymptotic behavior of elliptic, anisotropic singular perturbations problems

In this paper, we consider anitropic singular perturbations of some elliptic boundary value problems. We study the asymptotic behavior as [\varepsilon \rightarrow 0] for the solution. Strong convergence in some Sobolev spaces is proved and the rate of convergence in cylindrical domains is given

On a class of integro-differential problems

The paper is concerned with the existence of solutions to an integro-differential problem arising in the neutron transport theory. By an anisotropic singular perturbations method we show that solutions of such a problem exist and are close to those of some nonlocal elliptic problem. The existence of the solutions of the nonlocal elliptic problem with bounded data is ensured by the Schauder fixed point theorem. Then an asymptotic method is applied in the general case. The limits of the solutions of the nonlocal elliptic problems are solutions of our integro-differential problem

Problème de contact sans frottement-Dirichlet pour les équations de Laplace et de Lamé dans un polygone

International audienc

Modelling of 60 Co concentrations in the dissolved and particulate phases in the Loire estuary

International audienc