Related papers: Stable and high-order accurate finite difference m…
We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial…
We prove the unique solvability, passivity/conservativity and some regularity results of two mathematical models for acoustic wave propagation in curved, variable diameter tubular structures of finite length. The first of the models is the…
In this paper, we study the propagation and stability of nonlinear sound waves in accretion disks. Using the shearing box approximation, we derive the form of these waves using a semi-analytic approach and go on to study their stability.…
This article investigates the velocity dispersion and the spurious reflection of the viscoelastic wave that occur in the numerical integration of the viscoelastic wave equation. For this purpose, the classic finite element of two nodes,…
Discontinuous Galerkin methods of higher order are applied as temporal discretizations for the transient Navier--Stokes equations. The spatial discretization based on inf-sup stable pairs of finite element spaces is stabilised using a…
In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
Stability of a set of travelling wave solutions to the hyperbolic generalization of the convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.
We develop a mean-field model to examine the stability of a `quasi-2D suspension' of elongated particles embedded within a viscous membrane. This geometry represents several biological and synthetic settings, and we reveal mechanisms by…
The object of this study is to investigate the effect of viscosity on propagation of free-surface waves in an incompressible viscous fluid layer of arbitrary depth. While we provide a more detailed study of properties of linear surface…
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…
We study modulational stability and instability in the Whitham equation, combining the dispersion relation of water waves and a nonlinearity of the shallow water equations, and modified to permit the effects of surface tension and constant…
We address the spatial discretization of an evolution problem arising from the coupling of viscoelastic and acoustic wave propagation phenomena by employing a discontinuous Galerkin scheme on polygonal and polyhedral meshes. The coupled…
This chapter reviews and compares discontinuous Galerkin time-stepping methods for the numerical approximation of second-order ordinary differential equations, particularly those stemming from space finite element discretization of wave…
In this paper we consider wave viscoelastic equation with dynamic boundary condition in a bounded domain, we establish a general decay result of energy by exploiting the frequency domain method which consists in combining a contradiction…
We study the vibrational spectra and the specific heat of disordered systems using an effective hydrodynamic framework. We consider the contribution of diffusive modes, i.e. the 'diffusons', to the density of states and the specific heat.…
The analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process. To perform accurate numerical investigations by the finite differences or finite element method, one…
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…
A full viscous quantum hydrodynamic system for particle density, current density, energy density and electrostatic potential coupled with a Poisson equation in one dimensional bounded intervals is studied. First, the existence and…
A gradient-based method for shape optimization problems constrained by the acoustic wave equation is presented. The method makes use of high-order accurate finite differences with summation-by-parts properties on multiblock curvilinear…
This work presents a space-time isogeometric analysis of biharmonic wave problem, in contrast to the more common application of space-time methods to second order wave equations. We first establish the unique solvability of the continuous…