We consider a general nonselfadjoint second order scalar operator in planar domain such that one of the boundary components is obtained by an arbitrary irregular curving under assumption amplitude small. The Dirichlet or Neumann condition imposed on perturbed component, and remaining part boundary. prove norm resolvent convergence operators, estimate rate two norms, spectrum operators. In selfa...

We derive boundary conditions for the vorticity equation with solid wall boundaries. The formulation uses a Dirichlet condition for the normal component of vorticity, and Neumann type conditions for the tangential components. In a Galerkin (integral) formulation the tangential condition is natural, i.e. it is enforced by a right-hand side functional and does not impose a boundary constraint on ...

In this paper, the Al2O3-water nanofluid flow in laminar and turbulent flows inside tubes fitted with diamond-shaped turbulators is numerically modeled. The nanofluid flow is modeled by employing a two-phase mixture method and applying the constant heat flux boundary condition at tube walls. In the results, the effects of different parameters such as the geometry of turbulators, volume fraction...

The paper wishes to demonstrate that, in quantum systems with boundaries, different boundary conditions can lead to remarkably different physical behaviour. Our seemingly innocent setting is a one dimensional potential well that is divided into two halves by a thin separating wall. The two half wells are populated by the same type and number of particles and are kept at the same temperature. Th...

We derive boundary conditions for the vorticity equation with solid wall boundaries. The formulation uses a Dirichlet condition for the normal component of vorticity, and Neumann type conditions for the tangential components. In a Galerkin (integral) formulation the tangential condition is natural, i.e. it is enforced by a right-hand side functional and does not impose a boundary constraint on ...

Abstract. The problem of Rayleigh–Bénard convection with internal heat sources and a variable gravity field is treated. For the case of stress-free boundary conditions, it is proved that the principle of exchange of stabilities holds as long as the product of gravity field and the integral of the heat sources is nonnegative throughout the layer. The proof is based on the idea of a positive oper...

The paper is concerned with linear thermoelastic plate equations in a domain Ω: utt +∆u+∆θ = 0 and θt −∆θ −∆ut = 0 in Ω× (0,∞), subject to Dirichlet boundary condition: u|Γ = Dνu|Γ = θ|Γ = 0 and initial condition: (u, ut, θ)|t=0 = (u0, v0, θ0) ∈W 2 p,D(Ω)×Lp×Lp. Here, Ω is a bounded or exterior domain in R (n ≥ 2). We assume that the boundary Γ of Ω is a C hypersurface and we define W 2 p,D by ...

We show herein the uniform stability of a thermoelastic plate model with no added dissipative mechanism on the boundary (uniform stability of a thermoelastic plate with added boundary dissipation was shown in [J. LAGNESE, Boundary Stabilization of Twin Plates, SIAM Stud. Appl. Math. 10, SIAM, Philadelphia, PA, 1989], as was that of the analytic case—where rotational forces are neglected—in [Z. ...

We study a 2-phase free boundary problem for harmonic measure first considered by Kenig and Toro [KT06] and prove a sharp Hölder regularity result. The central difficulty is that there is no a priori non-degeneracy in the free boundary condition. Thus we must establish non-degeneracy by means of monotonicity formulae.

The problem of laminar, natural convection flow over a vertical f rus tum of a cone is treated in this paper. The thermal boundary condition at the wall include both the constant wall temperature and the constant wall heat flux cases. The governing differential equations are solved by a combinat ion of quasilinearization and finitedifference methods. Numerical solutions are obtained for a range...