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We consider existence and uniqueness for several examples of linear parabolic equations formulated on moving hypersurfaces. Specifically, we study in turn a surface heat equation, an equation posed on a bulk domain, a novel coupled…
This paper presents a characteristic-based flux partitioning for the semi-implicit time integration of atmospheric flows. Nonhydrostatic models require the solution of the compressible Euler equations. The acoustic time-scale is…
Space and time discretizations of parabolic differential equations with dynamic boundary conditions are studied in a weak formulation that fits into the standard abstract formulation of parabolic problems, just that the usual L^2(\Omega)…
Many time-dependent linear partial differential equations of mathematical physics and continuum mechanics can be phrased in the form of an abstract evolutionary system defined on a Hilbert space. In this paper we discuss a general framework…
We find time discretizations for the two ''second flows'' of the Ablowitz-Ladik hierachy. These discretizations are described by local equations of motion, as opposed to the previously known ones, due to Taha and Ablowitz. Certain…
Acoustic perturbations in a parallel relativistic flow of an inviscid fluid are considered. The general expression for the frequency of the sound waves in a uniformly (with zero shear) moving medium is derived. It is shown that relativity…
The subject of this paper is the consecutive procedure of discretization and quantization of two similar classical integrable systems in three-dimensional space-time: the standard three-wave equations and less known modified three-wave…
Within this paper, we introduce partially and fully decoupled time stepping schemes for linear thermo-poroelasticity. This means that the mechanics, heat, and flow equations can be solved sequentially. We provide sufficient conditions on…
Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in [17], is extended in this paper to include singular lower order terms, while keeping low initial regularity. The results are applied to…
We develop a unified theory for continuous in time finite element discretisations of partial differential equations posed in evolving domains including the consideration of equations posed on evolving surfaces and bulk domains as well…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum mechanics problems so that any property of the continuum that is proved using vector calculus can be proven in an analogous way…
Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
We consider the initial-value problem of abstract wave equations with weak dissipation. We show that under conditions on the dissipation coefficient and its derivative the solutions to the abstract dissipative equation are closely related…
We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…
We revisit the molecular arguments underpinning the Eulerian model for compressible and diffusive flows, and conclude that a heat diffusive term appears to be missing in the original model. By studying a pure heat transfer problem, we…
In this paper, we consider a linear heat equation with constant coefficients and a single constant delay. Such equations are commonly used to model and study various problems arising in ecology and population biology when describing the…
The 2-step staggered (also called leap-frog) time discretisation of linear 2nd-order Hamiltonian systems (typically linear elastodynamics in a stress-velocity form) is extended for a 3-step staggered discretisation applicable for systems…
We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation along trajectories operator…