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On non-overdetermined inverse scattering at zero energy in three dimensions

Roman G. Novikov (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We develop the ∂ ¯ -approach to inverse scattering at zero energy in dimensions d ≥ 3 of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction procedure, stability estimate and approximate reconstruction for the problem of finding a sufficiently small potential v in the Schrödinger equation from a fixed non-overdetermined (“backscattering” type) restriction h | Γ of the Faddeev generalized scattering amplitude h in the...

On the decomposition of particle size distribution in the extraction replica method

Vratislav Horálek (1981)

Aplikace matematiky

This paper deals with the method for evaluating exposures of nickel alloy structures containing both extracted and sectioned particles. The presented stereological model makes it possible to estimate two unknown spatial parameters, the mean value of the particle size distribution and the depth of etching with the use of the information obtained from the combined structure of the exposures.

On the temperature distribution in cold ice

James N. Flavin, Salvatore Rionero (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The linear heat equation predicts that the variations of temperature along a cold ice sheet {i.e. at a temperature less than is freezing point) due to a sudden increase in air temperature, are very very slow. Based on this we represent the nonlinear evolution of an ice sheet as a sequence of steady states. As a first fundamental indication that this model is correct well posedness with respect to the variations of initial and boundary data is proved. Further an estimate of the error made in evaluating...

On the two-dimensional compressible isentropic Navier–Stokes equations

Catherine Giacomoni, Pierre Orenga (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with γ = c p / c v = 2 . These equations also modelize the shallow water problem in height-flow rate formulation used to solve the flow in lakes and perfectly well-mixed sea. We establish a convergence result for the time-discretized problem when the momentum equation and the continuity equation are solved with the Galerkin method, without adding a penalization term in the continuity equation as it is made in...

On the two-dimensional compressible isentropic Navier–Stokes equations

Catherine Giacomoni, Pierre Orenga (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with γ = c p / c v = 2 . These equations also modelize the shallow water problem in height-flow rate formulation used to solve the flow in lakes and perfectly well-mixed sea. We establish a convergence result for the time-discretized problem when the momentum equation and the continuity equation are solved with the Galerkin method, without adding a penalization term in the continuity equation as it is made in Lions...

On the von Neumann problem and the approximate controllability of Stackelberg-Nash strategies for some environmental problems.

Jesús Ildefonso Díaz (2002)

RACSAM

Two problems arising in Environment are considered. The first one concerns a conjecture posed by von Neumann in 1955 on the possible modification of the albedo in order to control the Earth surface temperature. The second one is related to the approximate controllability of Stackelberg-Nash strategies for some optimization problems as, for instance, the pollution control in a lake. The results of the second part were obtained in collaboration with Jacques-Lois Lions.

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