Page 1 Mathematical Surveys and Monographs Volume 188 The Water Waves Problem
Mathematical Analysis and Asymptotics David Lannes American Mathematical Society Page 2 …

Integrated, process‐based numerical models in hydrology are rapidly evolving, spurred by
novel theories in mathematical physics, advances in computational methods, insights from …

These notes are devoted to the study of some problems related to shallow-water equations.
In particular, we will review results from derivations of shallow-water systems which depend …

Falling liquid films are examples of open flows which undergo a sequence of supercritical
instabilities giving way to a spatio-temporal weak disorder organized around interfacial …

Shallow landslides pose a significant threat to people and infrastructure. Despite significant
progress in the understanding of such phenomena, the evaluation of the size of the …

The shallow water equations are widely used to model the flow of a thin layer of fluid
submitted to gravity forces. They are usually formally derived from the full incompressible …

A formulation of the two-dimensional shallow water equations adapted to general and
complex terrains is proposed. Its derivation starts from the observation that the typical …

In this paper we propose a well-balanced finite volume/augmented Lagrangian method for
compressible visco-plastic models focusing on a compressible Bingham type system with …

The purpose of this paper is to derive rigorously the so-called viscous shallow-water
equations given for instance in [18, pp. 958-959]. Such a system of equations is similar to …

In this article, we present a model of heat transfer occurring through a liquid film flowing
down a vertical wall. This new model is formally derived using the method of asymptotic …