27 research outputs found
Long term behaviour of singularly perturbed parabolic degenerated equation
In this paper we consider models for short-term, mean-term and long-term
morphodynamics of dunes and megariples. We give an existence and uniqueness
result for long term dynamics of dunes. This result is based on a time-space
periodic solution existence result for degenerated parabolic equation that we
set out. Finally the mean-term and long-term models are homogenized
Singularly perturbed degenerated parabolic equations and application to seabed morphodynamics in tided environment
In this paper we build models for short-term, mean-term and long-term
dynamics of dune and megariple morphodynamics. They are models that are
degenerated parabolic equations which are, moreover, singularly perturbed. We,
then give an existence and uniqueness result for the short-term and mean-term
models. This result is based on a time-space periodic solution existence result
for degenerated parabolic equation that we set out. Finally the short-term
model is homogenized
Topological Derivative for Shallow Water Equations
Coastal erosion is a major and growing environmental problem describing the
movement of sand caused by tides, waves or currents. Several phenomena
contribute to the significant advance of the sea. These include climate change,
with rising sea levels due to the melting of ice at the Earth's poles, the
amplification of the tidal effect, leading to the transport of large masses of
sand, storms, etc. We contribute to this problem by using topological shape
optimization techniques applied to an PDE describing coastal erosion. We use
Shallow water equations as a model.Comment: 31 page
The Wade Formula and the oil price fluctuation: An Optimal Control Theory approach
By considering the Wade Formula, we propose a model to study the evolution of
the oil price per barrel. Our model shows that the policy of diversification of
the energy is to be supported. This model is proposed to see how it is possible
to control parameters so that the oil price should decrease
Two-Scale numerical simulation of sand transport problems
International audienceIn this paper we consider a model for short term dynamics of dunes in tidal area. We construct a Two-Scale Numerical Method based on the fact that the solution of the equation which has oscillations Two-Scale converges to the solution of a well-posed problem. This numerical method uses on Fourier series
Topological Optimization with the p-Laplacian Operator and an Application in Image Processing
We focus in this paper on the theoretical and numerical aspect os image processing. We consider a non linear boundary value problem (the p-Laplacian) from which we will derive the asymptotic expansion of the Mumford-Shah functional. We give a theoretical expression of the topological gradient as well as a numerical confirmation of the result in the restoration and segmentation of images