Related papers: On the dynamics of shallow ice sheets. Modelling a…
We present the results of a combined experimental and theoretical investigation of the surface-tension-driven coalescence of flexible structures. Specifically, we consider the dynamics of the rise of a wetting liquid between flexible sheets…
Time-dependent models of fluid motion in thin layers, subject to signed source terms, represent important sub-problems within climate dynamics. Examples include ice sheets, sea ice, and even shallow oceans and lakes. We address these…
The aim of this paper is to prove the existence of weak solution for a quasi-static evolution of thermo-visco-elastic model with Norton-Hoff law of plasticity. The dependence on temperature occurs both in the elastic constitutive equations…
We study a model describing the motion of the fluid in a lake, assuming inflow-outflow effects across the bottom, the porous coast and the inflows and outflows of rivers. We prove the global in time existence result for this model. The…
Propagation of elastic waves in damaged media (concrete, rocks) is studied theoretically and numerically. Such materials exhibit a nonlinear behavior, with long-time softening and recovery processes (slow dynamics). A constitutive model…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
Sea ice is a mushy layer, a porous material whose properties depend on the relative proportions of solid and liquid. The growth of sea ice is governed by heat transfer through the ice together with appropriate boundary conditions at the…
A continuum (Mullins-type) model is formulated for the isotropic evolution of a solid surface on which the mass transport occurs by oscillatory surface diffusion. The time-space oscillations of diffusivity are assumed to be induced by…
The evolution of surface layers of a glassy material heated by a laser pulse above the glass transition temperature and cooled by heat diffusion is considered as the flow of a stretchable viscous fluid. The strong dependence of viscosity on…
Europa's icy surface likely overlies an ocean, but the ice thickness is not known. Here we model the temporal growth of a Europan shell of pure ice subject to varying ice-ocean heat fluxes, ice rheologies, and internal heating rates. Both…
We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for…
The primary data which determine the evolution of glaciation are the bedrock elevation and the surface mass balance. From this data, which we assume is defined over a fixed land region, the glacier's geometry solves a free boundary problem…
A finite element method for the evolution of a two-phase membrane in a sharp interface formulation is introduced. The evolution equations are given as an $L^2$--gradient flow of an energy involving an elastic bending energy and a line…
It is shown how the combination of atomic deposition and nonlinear diffusion may lead, below a critical temperature, to the growth of nonuniform layers on a substrate. The dynamics of such a system is of the Cahn-Hilliard type, supplemented…
In this study, we propose an improved version of the nonlinear shallow water (or Saint-Venant) equations. This new model is designed to take into account the effects resulting from the large spacial and/or temporal variations of the seabed.…
We investigate impact of a sphere onto a floating elastic sheet and the resulting formation and evolution of wrinkles in the sheet. Following impact, we observe a radially propagating wave, beyond which the sheet remains approximately…
We prove the local well-posedness for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime.
We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…
We consider a disk-shaped thin elastic sheet bonded to a compliant sphere. (Our sheet can slip along the sphere; the bonding controls only its normal displacement.) If the bonding is stiff (but not too stiff), the geometry of the sphere…
An asymptotic interface equation for directional solidification near the absolute stabiliy limit is extended by a nonlocal term describing a shear flow parallel to the interface. In the long-wave limit considered, the flow acts…