Il modello di Klein e la Cosmologia.
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Influence of bottom topography on long water waves
Florent Chazel (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom topography, one for small variations in amplitude, and one for strong variations. Starting from the Zakharov formulation of this problem, we rigorously compute the asymptotic expansion of the involved Dirichlet-Neumann operator. Then, following the global strategy...
Instability of the stationary solutions of generalized dissipative Boussinesq equation
Amin Esfahani (2014)
Applications of Mathematics
In this work we study the generalized Boussinesq equation with a dissipation term. We show that, under suitable conditions, a global solution for the initial value problem exists. In addition, we derive sufficient conditions for the blow-up of the solution to the problem. Furthermore, the instability of the stationary solutions of this equation is established.
Integration of the EPDiff equation by particle methods
Alina Chertock, Philip Du Toit, Jerrold Eldon Marsden (2012)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
The purpose of this paper is to apply particle methods to the numerical solution of the EPDiff equation. The weak solutions of EPDiff are contact discontinuities that carry momentum so that wavefront interactions represent collisions in which momentum is exchanged. This behavior allows for the description of many rich physical applications, but also introduces difficult numerical challenges. We present a particle method for the EPDiff equation that is well-suited for this class of solutions and...
Integration of the EPDiff equation by particle methods∗∗∗∗∗∗
Alina Chertock, Philip Du Toit, Jerrold Eldon Marsden (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
The purpose of this paper is to apply particle methods to the numerical solution of the EPDiff equation. The weak solutions of EPDiff are contact discontinuities that carry momentum so that wavefront interactions represent collisions in which momentum is exchanged. This behavior allows for the description of many rich physical applications, but also introduces difficult numerical challenges. We present a particle method for the EPDiff equation that...
Invariant manifolds and alternative approaches to reduce perturbation theory: Dissipative systems.
Morris, Hedley C., Sheil, Derek, Dodd, Roger (1984)
International Journal of Mathematics and Mathematical Sciences
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