Related papers: Spectral Analysis of Diffusions with Jump Boundary
We study the influence of the boundary conditions at the solid liquid interface on diffusion in a confined fluid. Using an hydrodynamic approach, we compute numerical estimates for the diffusion of a particle confined between two planes.…
A singularly perturbed parabolic problem of convection-diffusion type with incompatible inflow boundary and initial conditions is examined. In the case of constant coefficients, a set of singular functions are identified which match certain…
We study the spectral flow of Landau-Robin hamiltonians in the exterior of a compact domain with smooth boundary. This provides a method to study the spectrum of the exterior Landau-Robin hamiltonian's dependence on the choice of Robin…
The choice of boundary condition makes an essential difference in the solution structure of diffusion equations. The Dirichlet and Neumann boundary conditions and their combination have been the most used, but their legitimacy has been…
We consider a planar waveguide with combined Dirichlet and Neumann conditions imposed in a "twisted" way. We study the discrete spectrum and describe it dependence on the configuration of the boundary conditions. In particular, we show that…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
We study the initial-boundary value problem for the Hamilton-Jacobi equation with nonlinear diffusion $u_t=\Delta_p u+|\nabla u|^q$ in a two-dimensional domain for $q>p>2$. It is known that the spatial derivative of solutions may become…
In this work we mainly prove the existence and pathwise uniqueness of solutions to general backward doubly stochastic differential equations with jumps appearing in both forward and backward integral parts. Several comparison theorems under…
In this paper we show existence of solutions for some elliptic problems with nonlocal diffusion by means of nonvariational tools. Our proof is based on the use of topological degree, which requires a priori bounds for the solutions. We…
We present a meshfree generalized finite difference method for solving Poisson's equation with a diffusion coefficient that contains jump discontinuities up to several orders of magnitude. To discretize the diffusion operator, we formulate…
The paper deals with first order self-adjoint elliptic differential operators on a smooth compact oriented surface with non-empty boundary. We consider such operators with self-adjoint local boundary conditions. The paper is focused on…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
For positive recurrent jumping-in diffusions with small jumps, we establish distributional limits of the fluctuations of inverse local times and occupation times. For this purpose, we introduce and utilize eigenfunctions with modified…
'A basic and basically unsolved problem in fluid dynamics is to determine the evolution of rising bubbles and falling drops of one miscible liquid in another' [1]. Here, we address this important literature gap and present the first theory…
Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem.…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
We investigate singularly perturbed elliptic problems with multiplicative nonlocal diffusion terms subject to Robin boundary conditions. The diffusion depends on a global quantity of the solution, which introduces a nonlocal coupling…
We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of…
We study the $L^2$ spectral gap of a large system of strongly coupled diffusions on unbounded state space and subject to a double-well potential. This system can be seen as a spatially discrete approximation of the stochastic Allen-Cahn…
We consider parametric estimation of the continuous part of a class of ergodic diffusions with jumps based on high-frequency samples. Various papers previously proposed threshold based methods, which enable us to distinguish whether…