### A bifurcation result for Sturm-Liouville problems with a set-valued term.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

In this paper we introduce the equations of a layered quasi-geostrophic ocean model, and the corresponding data assimilation problem. We first give the variational formulation. We then point out the linear theory of duality. Finally, we apply duality to our nonlinear model by describing an algorithm to solve the data assimilation problem, introducing a dual cost function and a simple way to compute its gradient.

We present some results on the mathematical treatment of a global two-dimensional diffusive climate model. The model is based on a long time averaged energy balance and leads to a nonlinear parabolic equation for the averaged surface temperature. The spatial domain is a compact two-dimensional Riemannian manifold without boundary simulating the Earth. We prove the existence of bounded weak solutions via a fixed point argument. Although, the uniqueness of solutions may fail, in general, we give a...

In the present article, an attempt is made to derive optimal data-driven machine learning methods for forecasting an average daily and monthly rainfall of the Fukuoka city in Japan. This comparative study is conducted concentrating on three aspects: modelling inputs, modelling methods and pre-processing techniques. A comparison between linear correlation analysis and average mutual information is made to find an optimal input technique. For the modelling of the rainfall, a novel hybrid multi-model...

A nonstandard approach to change point estimation is presented in this paper. Three models with random coefficients and Bayesian approach are used for modelling the year average temperatures measured in Prague Klementinum. The posterior distribution of the change point and other parameters are estimated from the random samples generated by the combination of the Metropolis-Hastings algorithm and the Gibbs sampler.

L’objectif de cet article est d’illustrer la nature multi-échelle de quelques systèmes naturels en sciences de l’univers. Nous nous intéressons tout d’abord à l’onde circumpolaire Antarctique, une des manifestations les plus marquantes de la variabilité australe. Sa variabilité est analysée à partir de relevés de stations de météorologie côtières du continent Antarctique, fournissant des données de température depuis 1955. Grâce à une « décomposition modale empirique » (DME) couplée à une analyse...

The objective of this work is to obtain theoretical estimates on the large and small scales for geophysical flows. Firstly, we consider the shallow water problem in the one-dimensional case, then in the two-dimensional case. Finally we consider geophysical flows under the hydrostatic hypothesis and the Boussinesq approximation. Scale separation is based on Fourier series, with N models in each spatial direction, and the choice of a cut-off level N1 < N to define large and small scales. We...