Related papers: Boundary Conditions as Dynamical Fields
Boundary conditions dictate how fluids, including liquid crystals, flow when pumped through a channel. Can boundary conditions also be used to control internally driven active fluids that generate flows spontaneously? By using numerical…
In recent decades, considerable research has been devoted to partial differential equations (PDEs) with dynamic boundary conditions. However, the physical interpretation of the parameters involved often remains unclear, which in turn limits…
A relativistic equation is proposed for the bound state of two particles, which is in accord with the boundary condition for the propagation of the negative-energy states and reduces to the (one-body)Dirac equation in the infinite limit of…
A boundary control problem for the pure Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved. Key words: Cahn-Hilliard equation,…
(i) Uncountably many synchronized reflected Brownian motions can hit the boundary of a $C^2$ domain at the same time. (ii) Measures associated to local times of two synchronized reflected Brownian motions are mutually singular until the…
We investigate classical solutions of nonlinear elliptic equations with two classes of dynamical boundary conditions, of reactive and reactive-diffusive type. In the latter case it is shown that well-posedness is to a large extent…
This paper deals with the heat equation posed in a bounded regular domain coupled with a dynamical boundary condition of reactive-diffusive type, involving the Laplace-Beltrami operator. We prove well-posedness of the problem together with…
We develop a new technique for studying the boundary limiting behavior of a holomorphic function on a domain $\Omega$ -- both in one and several complex variables. The approach involves two new localized maximal functions. As a result of…
Writing the boundary integral equation for an exterior problem of elasticity is subordinate so far to hypotheses on the asymptotical behaviour at infinity of solutions. The sufficient conditions met in the literature are too restrictive and…
We study admissible boundary conditions for a charged quantum particle in a two-dimensional region subjected to an external magnetic field, i.e. a quantum magnetic billiard. After reviewing some physically interesting classes of admissible…
On a class of four-dimensional Lifshitz spacetimes with critical exponent $z=2$, including a hyperbolic and a spherical Lifshitz topological black hole, we consider a real Klein-Gordon field. Using a mode-decomposition, we split the…
A simple transformation converts a solution of a partial differential equation with a Dirichlet boundary condition to a function satisfying a Robin (generalized Neumann) condition. In the simplest cases this observation enables the exact…
We consider one-dimensional stochastic differential equations with a boundary condition, driven by a Poisson process. We study existence and uniqueness of solutions and the absolute continuity of the law of the solution. In the case when…
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.
We consider parabolic equations with mixed boundary conditions and domain inhomogeneities supported on a lower dimensional hypersurface, enforcing a jump in the conormal derivative. Only minimal regularity assumptions on the domain and the…
Lyapunov functions are popularly used to investigate the stabilization problem of systems of hyperbolic conservation laws with boundary controls. In real life applications often not every boundary value can be observed. In this work, we…
An exact analytic solution is obtained for a uniformly expanding, neutral, infinitely conducting plasma sphere in an external dipole magnetic field. The electrodynamical aspects related to the radiation and transformation of energy were…
A new method to compute the symplectic structure of a quantum field theory with non trivial boundary conditions is proposed. Following the suggestion in \cite{ho:gnus, ardalan}, we regard that the boundary conditions are second class…
In many applications, transport of particles can be described by the diffusion equation, or its convective-diffusion generalizations, in part of three-dimensional space. In particular, in surface deposition or in growth of aggregates or…
The well-posedness of a system of partial differential equations and dynamic boundary conditions, both of Cahn-Hilliard type, is discussed. The existence of a weak solution and its continuous dependence on the data are proved using a…