Related papers: A stationary free boundary problem modeling electr…
Plasma-boundaries floating in an ionized gas are usually negatively charged. They accumulate electrons more efficiently than ions which leads to the formation of a quasi-stationary electron film at the boundaries. We propose, in a…
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…
Local well-posedness for a nonlinear parabolic-hyperbolic coupled system modelling Micro-Electro-Mechanical System (MEMS) is studied. The particular device considered is a simple capacitor with two closely separated plates, one of which has…
In this paper, we study a nonlinear boundary diffusion equation of porous medium type arising from a boundary control problem. We give a complete and sharp characterization of the asymptotic behavior of its solutions, and prove the…
In this paper, we study a free boundary problem modeling solid tumor growth with vasculature which supplies nutrients to the tumor; this is characterized in the Robin boundary condition. It was recently established [Discrete Cont. Dyn.…
The purpose of this work is to review the status about stationary solutions of the axially symmetric Einstein-Vlasov system with a focus on open problems of both analytical and numerical nature. For the latter we emphasize that the code…
We develop an athermal shear-transformation-zone (STZ) theory of plastic deformation in spatially inhomogeneous, amorphous solids. Our ultimate goal is to describe the dynamics of the boundaries of voids or cracks in such systems when they…
The instabilities arising in a one-dimensional beam sustained by the diffusive photorefractive nonlinearity in out-of-equilibrium ferroelectrics are theoretically and numerically investigated. In the "scale-free model", in striking contrast…
Utilising Onsager's variational formulation, we derive dynamical equations for the relaxation of a fluid membrane tube in the limit of small deformation, allowing for a contrast of solvent viscosity across the membrane and variations in…
This work is part of a general study on the long-term safety of the geological repository of nuclear wastes. A diffusion equation with a moving free boundary in one dimension is introduced and studied. The model describes some mechanisms…
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.…
Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds…
We study a class of semilinear free boundary problems in which admissible functions $u$ have a topological constraint, or spanning condition, on their 1-level set. This constraint forces $\{u=1\}$, which is the free boundary, to behave like…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
We attempt to describe surface defects in smectic A thin films by formulating a free discontinuity problem - that is, a variational problem in which the order parameter is allowed to have jump discontinuities on some (unknown) set. The free…
We first give a complete linearized stability analysis around stationary solutions of the Mullins-Sekerka flow with $90^\circ$ contact angle in two space dimensions. The stationary solutions include flat interfaces, as well as arcs of…
Motivated by experiments in electroconvection in nematic liquid crystals with homeotropic alignment we study the coupled amplitude equations describing the formation of a stationary roll pattern in the presence of a weakly-damped mode that…
In this paper we discuss the Mather problem for stationary Lagrangians, that is Lagrangians $L:\Rr^n\times \Rr^n\times \Omega\to \Rr$, where $\Omega$ is a compact metric space on which $\Rr^n$ acts through an action which leaves $L$…
The effects of electromagnetic vacuum fluctuations with the boundary on charged particles is investigated. They may be observed via an electron interference experiment near the conducting plate, where boundary effects of vacuum fluctuations…
We propose a numerical method to approximate viscosity solutions of fully nonlinear free transmission problems. The method discretises a two-layer regularisation of a PDE, involving a functional and a vanishing parameter. The former is…