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Si prova l'esistenza di un'unica soluzione debole che dipende con continuità dai dati al contorno per il problema lineare di Molodenskii in approssimazione quasi sferica, nel caso che la superficie al contorno soddisfi una condizione di cono. Si segue un approccio costruttivo diretto, che generalizza una procedura precedentemente elaborata per il problema semplice di Molodenskii. Inoltre si prova che la soluzione ha derivate prime a quadrato integrabile al contorno, il che è essenziale per le applicazioni...
Si studiano le condizioni per 1’esistenza, l’unicità e la stabilità della soluzione debole del problema lineare di Molodenskii in approssimazione quasi-sferica, generalizzando una tecnica perturbativa usata in precedenza per la soluzione di tipo classico. La procedura seguita richiede delle condizioni di maggior regolarità per il contorno, di quelle usate nell’analisi del problema «semplice». Il risultato ottenuto è l'esistenza e unicità di una soluzione con derivate seconde a quadrato integrabile,...
The elastic behaviour of the Earth, including its eigenoscillations, is usually described by the Cauchy-Navier equation. Using a standard approach in seismology we apply the Helmholtz decomposition theorem to transform the Fourier transformed Cauchy-Navier equation into two non-coupled Helmholtz equations and then derive sequences of fundamental solutions for this pair of equations using the Mie representation. Those solutions are denoted by the Hansen vectors Ln,j, Mn,j, and Nn,j in geophysics....
Deterministic and stochastic approach to modeling common trends has been applied to time series of horizontal coordinates of the permanent GPS station Modra – Piesky (recorded weekly during the period of 4 years).
This article presents a survey of a new dynamical systems theory for 2D incompressible flows and its applications to geophysical fluid dynamics.
In this paper, we consider a 2D mathematical modelling of the vertical compaction effect in a water saturated sedimentary basin. This model is described by the usual conservation laws, Darcy’s law, the porosity as a function of the vertical component of the effective stress and the Kozeny-Carman tensor, taking into account fracturation effects. This model leads to study the time discretization of a nonlinear system of partial differential equations. The existence is obtained by a fixed-point argument....
In this paper, we consider a 2D mathematical modelling of the vertical
compaction effect in a water saturated sedimentary basin. This model is
described by the usual conservation laws, Darcy's law, the porosity as a
function of the vertical component of the effective stress and the
Kozeny-Carman tensor, taking into account fracturation effects. This model
leads to study the time discretization of a nonlinear system of
partial differential equations. The existence is obtained by a fixed-point
argument....
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