Navier–Stokes–Fourier system with Dirichlet boundary conditions

Absorption semigroups and dirichlet boundary conditions

TECHNISCHE UNIVERSITÄT BERLIN Moving Dirichlet Boundary Conditions

This paper develops a framework to include Dirichlet boundary conditions on a subset of the boundary which depends on time. In this model, the boundary conditions are weakly enforced with the help of a Lagrange multiplier method. In order to avoid that the ansatz space of the Lagrange multiplier depends on time, a bi-Lipschitz transformation, which maps a fixed interval onto the Dirichlet bound...

Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions

when ε ≥ 0 is small. In particular, ∆2v + εv ≥ 0 in Ω, with v = ∆v = 0 on ∂Ω, implies v ≥ 0 for ε small. In numerical experiments ([14]) for one dimension a similar behaviour was observed under Dirichlet boundary conditions v = ∂ ∂nv = 0. In this paper we will derive a 3-G type theorem as in (1) but with G1,n replaced by the Green function Gm,n for the m-polyharmonic operator with Dirichlet bou...

Dynamical Casimir effect with Dirichlet and Neumann boundary conditions

We derive the radiation pressure force on a non-relativistic moving plate in 1+1 dimensions. We assume that a massless scalar field satisfies either Dirichlet or Neumann boundary conditions (BC) at the instantaneous position of the plate. We show that when the state of the field is invariant under time translations, the results derived for Dirichlet and Neumann BC are equal. We discuss the forc...

Stochastic Partial Differential Equations with Dirichlet White-noise Boundary Conditions

– The paper is devoted to one-dimensional nonlinear stochastic partial differential equations of parabolic type with non homogeneous Dirichlet boundary conditions of white-noise type. We formulate a set of conditions that a random field must satisfy to solve the equation. We show that a unique solution exists and that we can write it in terms of the stochastic kernel related to the problem. Thi...