Related papers: Long time behavior of solutions to the generalized…
In this paper we deal with the long time existence for the Cauchy problem associated to some asymptotic models for long wave, small amplitude gravity surface waves. We generalize some of the results that can be found in the literature…
In this paper a three-parameter family of Boussinesq systems is studied. The systems have been proposed as models of the propagation of long internal waves along the interface of a two-layer system of fluids with rigid-lid condition for the…
Consideration is given to the influence of an underwater landslide on waves at the surface of a shallow body of fluid. The equations of motion which govern the evolution of the barycenter of the landslide mass include various dissipative…
This study deals with higher-ordered asymptotic equations for the water-waves problem. We considered the higher-order/extended Boussinesq equations over a flat bottom topography in the well-known long wave regime. Providing an existence and…
In this paper, we investigate the well-posedness of a nonlinear dispersive model with variable coefficients that describes the evolution of surface waves propagating through a one-dimensional shallow water channel of finite length with…
We prove in this paper a long time existence result for a modified Boussinesq-Peregrine equation in one dimension, describing the motion of Water Waves in shallow water, in the case of a non flat bottom. We first give a local existence…
In this paper, we study the nonlinear dissipative Boussinesq equation in the whole space $\mathbb{R}^n$ with $L^1$ integrable data. As our preparations, the optimal estimates as well as the optimal leading terms for the linearized model are…
In this paper we deal with the long time existence for the Cauchy problem associated to BBM-type Boussinesq systems of equations which are asymptotic models for long wave, small amplitude gravity surface water waves. As opposed to previous…
The travelling wave problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This system firstly appeared in [Dinvay, Dutykh, Kalisch 2018], where it was numerically shown to be stable and…
We prove the existence on long time scales of the solutions to the Cauchy problem for a version of weakly transverse Boussinesq systems arising in the modeling of surface water waves. This system is much more complicated than the isotropic…
Considered here is a class of Boussinesq systems of Nwogu type. Such systems describe propagation of nonlinear and dispersive water waves of significant interest such as solitary and tsunami waves. The initial-boundary value problem on a…
Boussinesq-type wave equations involve nonlinearities and dispersion. In this paper a Boussinesq-type equation with amplitude-dependent nonlinearities is presented. Such a model was proposed by Heimburg and Jackson (2005) for describing…
In this article we consider the Boussinesq system supplemented with some dissipation terms. These equations model the propagation of a waterwave in shallow water. We prove the existence of a global smooth attractor for the corresponding…
The numerical approximation of some Boussinesq systems in two spatial dimensions is here considered. The differential systems under study are proposed as asymptotic models for the propagation of waves along the interface of two layers of…
The aim of this paper is to present a survey and a detailed numerical study on a remarkable Boussinesq system describing weakly nonlinear, long surface water waves. In the one-dimensional case, this system can be viewed as a dispersive…
We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonnegative. Some well-known examples of…
Considered here are Boussinesq systems of equations of surface water wave theory over a variable bottom. A simplified such Boussinesq system is derived and solved numerically by the standard Galerkin-finite element method. We study by…
In this paper we study some theoretical and numerical issues of the Boussinesq/Full dispersion system. This is a a three-parameter system of pde's that models the propagation of internal waves along the interface of two-fluid layers with…
This paper is a continuation of a previous work by two of the Authors on long time existence for Boussinesq systems modeling the propagation of long, weakly nonlinear water waves. We provide proofs on examples not considered previously in…
A century and a half ago, J. Boussinesq derived an equation for the propagation of water waves in a channel. Despite the fundamental importance of this equation for a number of physical phenomena, mathematical results on it remain scarce.…