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DCDS-B

In the case of a constant depth, western intensification of currents in
oceanic basins was mathematically recovered in various models (such as
Stommel, Munk or quasi-geostrophic ones) as a boundary layer
appearing when the solution of equations converges to the solution of a
pure transport equation.
This convergence is linked to the fact that any characteristic
line of the transport vector field included in the equations crosses the
boundary, and the boundary layer is located at outgoing points.

Here we recover such a boundary layer for the vertical-geostrophic model with a general bathymetry. More precisely, we allow depth to vanish on the shore in which case the above mentioned characteristic lines no longer cross the boundary. However a boundary layer still appears because the transport vector field $a$ (which is tangential to the boundary) locally converges to a vector field $\overline{a}$ with characteristic lines crossing the boundary.

Here we recover such a boundary layer for the vertical-geostrophic model with a general bathymetry. More precisely, we allow depth to vanish on the shore in which case the above mentioned characteristic lines no longer cross the boundary. However a boundary layer still appears because the transport vector field $a$ (which is tangential to the boundary) locally converges to a vector field $\overline{a}$ with characteristic lines crossing the boundary.

PROC

In this article, we present a new continuous model for tumor growth. This model describes the evolution of three components: sane tissue, cancer cells and extracellular medium. In order to render correctly the cellular division, this model uses a discrete description of the cell cycle (the set of steps a cell has to undergo in order to divide). To account for cellular adhesion and the mechanics which may influence the growth, we assume a viscoelastic mechanical behavior. This model extends the one presented in [18] with a more realistic description of the forces that drive the movement.

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