Related papers: Tsunami propagation for singular topographies
Wave shoaling of water waves over mild bottom slopes is well described by linearized theories. However, the analytical treatment of nonlinear wave shoaling subject to rapidly varying bottoms has proven to be elusive in the past decades. As…
Given a Hilbert space, we investigate the well-posedness of the Cauchy problem for the wave equation for operators with discrete non-negative spectrum acting on it. We consider the cases when the time-dependent propagation speed is regular,…
The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV…
We construct numerically solitary wave solutions of the Rosenau equation using the Petviashvili iteration method. We first summarize the theoretical results available in the literature for the existence of solitary wave solutions. We then…
Modeling the subgrid-scale dynamics of reduced models is a long standing open problem that finds application in ocean, atmosphere and climate predictions where direct numerical simulation (DNS) is impossible. While neural networks (NNs)…
Traveling waves for the FPU chain are constructed by solving the associated equation for the spatial profile $u$ of the wave. We consider solutions whose derivatives $u'$ need not be small, may change sign several times, but decrease at…
We analyse an algorithm of transition between Cauchy problems for second-order wave equations and first-order symmetric hyperbolic systems in case the coefficients as well as the data are non-smooth, even allowing for regularity below the…
In this paper, we study two-dimensional steady solitary gravity waves propagating along the surface of a fluid of finite depth. In particular, we can deal with general vorticity distributions and overhanging wave profiles. By conformal…
Covariant equations characterizing the strength of a singularity in spherical symmetry are derived and several models are investigated. The difference between central and non-central singularities is emphasised. A slight modification to the…
We study the flow of water waves over bathymetry that varies periodically along one direction. We derive a linearized, homogenized model and show that the periodic bathymetry induces an effective dispersion, distinct from the dispersion…
Here I present a general formulation of water wave propagation and scattering over topographical bottoms. A simple equation is found and is compared with existing theories. As an application, the theory is extended to the case of water…
In this note two blow-up results are proved for a weakly coupled system of semilinear wave equations with distinct scale-invariant lower order terms both in the subcritical case and in the critical case, when the damping and the mass terms…
To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the…
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be…
We study the behavior of shallow water waves propagating over bathymetry that varies periodically in one direction and is constant in the other. Plane waves traveling along the constant direction are known to evolve into solitary waves, due…
The Cauchy problem is considered for the perturbed strictly hyperbolic 2x2 system of quasilinear equations. The unperturbed problem has a persistent solution with two discontinuity lines (shock waves). Both an asymptotics of shock waves…
This expository note gives a digest version of Hormander's propagation of singularities theorem for the wave equation.
This paper presents two remarkable phenomena associated with the heat equation with a time delay: namely, the propagation of singularities and periodicity. These are manifested through a distinctive mode of propagation of singularities in…
To date it has not been possible to prove whether or not the three-dimensional incompressible Euler equations develop singular behaviour in finite time. Some possible singular scenarios, as for instance shock-waves, are very important from…
Long linear wave transformation in the basin of varying depth is studied for a case of a convex bottom profile in the framework of one-dimensional shallow water equation. The existence of travelling wave solutions in this geometry and the…