Related papers: A class of unstable free boundary problems
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…
In this work we demonstrate that a class of some one and two phase free boundary problems can be recast as nonlocal parabolic equations on a submanifold. The canonical examples would be one-phase Hele Shaw flow, as well as its two-phase…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
Existence of solution and stability results on a class of Non Linear Schroedinger type equations with a bounded nonlinearity are obtained, for a bounded domain and with Dirichlet boundary conditions. The kind of stability under discussion…
We consider a non-local free energy functional, modelling a competition between entropy and pairwise interactions reminiscent of the second order virial expansion, with applications to nematic liquid crystals as a particular case. We build…
The study of singular perturbations of the Dirichlet energy is at the core of the phenomenological-description paradigm in soft condensed matter. Being able to pass to the limit plays a crucial role in the understanding of the…
We study an initial-boundary-value problem of a nonlinear Korteweg-de Vries equation posed on a finite interval (0,2pi). The whole system has Dirichlet boundary condition at the left end-point, and both of Dirichlet and Neumann homogeneous…
In this paper, we shall study the Dirichlet problem for the minimal surfaces equation. We prove some results about the boundary behaviour of a solution of this problem. We describe the behaviour of a non-converging sequence of solutions in…
We consider non-local in time semilinear subdiffusion equations on a bounded domain, where the kernel in the integro-differential operator belongs to a large class, which covers many relevant cases from physics applications, in particular…
A class of diffusion driven Free Boundary Problems is considered which is characterized by the initial onset of a phase and by an explicit kinematic condition for the evolution of the free boundary. By a domain fixing change of variables it…
In this paper, we deal with the initial value problem for a class of fully nonlinear parabolic equations with a singular Dirichlet boundary condition in one space dimension. The interior equation includes, for example, a fully nonlinear…
In the classical homogeneous one-phase Bernoulli-type problem, the free boundary consists of a "regular" part and a "singular" part, as Alt and Caffarelli have shown in their pioneer work (J. Reine Angew. Math., 325, 105-144, 1981) that…
The dynamics of a free boundary problem for electrostatically actuated microelectromechanical systems (MEMS) is investigated. The model couples the electric potential to the deformation of the membrane, the deflection of the membrane being…
In this paper we argue that boundary condition may run with energy scale. As an illustrative example, we consider one-dimensional quantum mechanics for a spinless particle that freely propagates in the bulk yet interacts only at the origin.…
We consider an incompressible Bingham flow in a thin domain with rough boundary, under the action of given external forces and with no-slip boundary condition on the whole boundary of the domain. In mathematical terms, this problem is…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
The nonlocal models of peridynamics have successfully predicted fractures and deformations for a variety of materials. In contrast to local mechanics, peridynamic boundary conditions must be defined on a finite volume region outside the…
This is a study of a class of nonlocal nonlinear diffusion equations. We present a strong maximum principle for nonlocal time-dependent Dirichlet problems. Results are for bounded functions of space, rather than (semi)-continuous functions.…
We consider a large mass limit of the non-local isoperimetric problem with a repulsive Yukawa potential in two space dimensions. In this limit, the non-local term concentrates on the boundary, resulting in the existence of a critical regime…
Attention in the literature has increasingly turned to the issue of the dependence on ensemble and boundary conditions of fluctuation-induced forces. We have recently investigated this problem in the one-dimensional Ising model with…