Related papers: Conservation laws for free-boundary fluid layers
In studies of interfaces with dynamic chemical composition, bulk and interfacial quantities coupled via surface conservation laws of excess surface quantities. While this approach is for microscopically sharp interfaces, its applicability…
We study the hydrodynamic behaviour of the symmetric zero-range process on the finite interval $\{1, \ldots, N-1\}$ in contact with slow reservoirs at the boundary. Particles are injected and removed at sites $1$ and $N-1$ at rates that…
Atmospheric systems incorporating thermal dynamics must be stable with respect to both energy and entropy. While energy conservation can be enforced via the preservation of the skew-symmetric structure of the Hamiltonian form of the…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
Shallow flow or thin liquid film models are used for a wide range of physical and engineering problems. Shallow flow models allow capturing the free surface of the fluid with little effort and reducing the three-dimensional problem to a…
The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary…
A modular fluid-flow model for network congestion analysis and control is proposed. The model is derived from an information conservation law stating that the information is either in transit, lost or received. Mathematical models of…
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is…
Boundaries occur naturally in kinetic equations and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions…
We study a linear problem that arises in the study of dynamic boundaries, in particular in free boundary problems in connection with fluid dynamics. The equations are also very natural and of interest on their own.
The study of global-in-time dynamics of vacuum is crucial for understanding viscous flows. In particular, physical vacuum, characterized by a moving boundary with nontrivial finite normal acceleration, naturally arises in the motion of…
In numerical ocean models coast lines change the direction from one grid cell to its neighbor and the value for viscosity is set to be as small as possible. Therefore, model simulations are not converged with resolution and boundary…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
In this article, we consider scalar conservation laws with fluxes having spatial discontinuities and possible flat regions and study the following three aspects: (i) existence, (ii) uniqueness and (iii) BV regularity of solutions. We…
We consider a nonlinear, free boundary fluid-structure interaction model in a bounded domain. The viscous incompressible fluid interacts with a nonlinear elastic body on the common boundary via the velocity and stress matching conditions.…
In this work, we derive asymptotic interface models for an elastic Muskat free boundary problem describing Darcy flow beneath an elastic membrane. In a weakly nonlinear regime of small interface steepness, we obtain nonlocal evolution…
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 consider the dynamics of lattices which have constrained constitutive units flexible in only their mutual orientations. A continuum description is derived through which it is shown that the models have zero shear velocity, free-particle…
In this paper we study the long time dynamics of the solutions to the initial-boundary value problem for a scalar conservation law with a saturating nonlinear diffusion. After discussing the existence of a unique stationary solution and its…
We focus on a family of nonlinear continuity equations for the evolution of a non-negative density $\rho$ with a continuous and compactly supported nonlinear mobility $\mathrm{m}(\rho)$ not necessarily concave. The velocity field is the…