Éditeur(s) : HAL CCSD
Résumé : International audience
This paper deals with variational inclusions of the form 0 2 f(x) + g(x) K where f is smooth function from a re exive Banach space X into a Banach space Y , g is a Lipschitz function from X into Y and K is a nonempty closed convex cone in the space Y . We show that the previous problem can be solved by an extension of the Zincenko's method which can be seen as a perturbed Newton's method. Numerical results are given at the end of the paper.
Revista Investigacion Operacional

hal-00924143
https://hal.archives-ouvertes.fr/hal-00924143

Éditeur(s) : HAL CCSD
Résumé : International audience
This paper deals with variational inclusions of the form 0 ∈ K − f(x) − g(x) where f is a smooth function from a reflexive Banach space X into a Banach space Y , g is a function from X into Y admitting divided differences and K is a nonempty closed convex cone in the space Y . We show that the previous problem can be solved by a combination of two methods: the Newton and the Secant methods. We show that the order of the semilocal method obtained is equal to (1 + √5)/2. Numerical results are also given to illustrate the convergence at the end of the paper.
Serdica Math. J.

hal-00924150
https://hal.archives-ouvertes.fr/hal-00924150

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The growth of relief in active tectonic areas is mainly controlled by the interactions between tectonics and surface processes (erosion and sedimentation). The study of long-lived morphologic markers formed by these interactions can help in quantifying the competing effects of tectonics, erosion and sedimentation. In regions experiencing active extension, river-long profiles and faceted spurs (triangular facets) can help in un- derstanding the development of mountainous topography along normal fault scarps. In this study, we devel- oped analogue experiments that simulate the morphologic evolution of a mountain range bounded by a normal fault. This paper focuses on the effect of the fault slip rate on the morphologic evolution of the foot- wall by performing three analogue experiments with different fault slip rates under a constant rainfall rate. A morphometric analysis of the modelled catchments allows comparing with a natural case (Tunka half- graben, Siberia). After a certain amount of fault slip, the modelled footwall topographies of our models reaches a dynamic equilibrium (i.e., erosion balances tectonic uplift relative to the base level) close to the fault, whereas the topography farther from the fault is still being dissected due to regressive erosion. We show that the rates of vertical erosion in the area where dynamic equilibrium is reached and the rate of re- gressive erosion are linearly correlated with the fault throw rate. Facet morphology seems to depend on the fault slip rate except for the fastest experiment where faceted spurs are degraded due to mass wasting. A stream-power law is computed for the area wherein rivers reach a topographic equilibrium. We show that the erosional capacity of the system depends on the fault slip rate. Finally, our results demonstrate the pos- sibility of preserving convex river-long profiles on the long-term under steady external (tectonic uplift and rainfall) conditions.
ISSN: 0040-1951

hal-00646966
https://hal.archives-ouvertes.fr/hal-00646966
https://hal.archives-ouvertes.fr/hal-00646966/document
https://hal.archives-ouvertes.fr/hal-00646966/file/preprint_Strak_2011.pdf
DOI : 10.1016/j.tecto.2011.10.005