This paper considers the stabilization of a heat equation with an integral type nonlocal boundary condition. Via choosing new intermediate target control system undetermined term instead determined one appeared in normal backstepping method, we convert original into by transformation. At same time, prove exponential Lyapunov function method after appropriate linear feedback control. Then, combi...

We consider in this paper the mathematical and numerical modelling of reflective boundary conditions (BC) associated to Boltzmann Poisson systems, including diffusive reflection in addition to specularity, in the context of electron transport in semiconductor device modelling at nano scales, and their implementation in Discontinuous Galerkin (DG) schemes. We study these BC on the physical bound...

Motivated by the partial differential equations of mixed type that arise in the reduction of the Einstein equations by a helical Killing vector field, we consider a boundary value problem for the helically-reduced wave equation with an arbitrary source in 2+1 dimensional Minkowski spacetime. The reduced equation is a second-order partial differential equation which is elliptic inside a disk and...

In this paper we study the stability of finite difference approximations to initial-boundary hyperbolic systems. As is well-known, a proper specification of boundary conditions for such systems is essential for their solutions to be well-defined. We prove a discrete analogue of the above if the numerical boundary conditions are consistent with an inflow part of the problem, they render the over...

Motivated by the paraxial narrow–angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a general Schrödinger-type equation posed on two-dimensional variable domains with mixed boundary conditions. The resulting initialand boundary-value problem is transformed into an equivalent one posed on a ...

We analyze the well-posedness of a flow-plate interaction considered in [22, 24]. Specifically, we consider the Kutta-Joukowski boundary conditions for the flow [20, 28, 26], which ultimately give rise to a hyperbolic equation in the half-space (for the flow) with mixed boundary conditions. This boundary condition has been considered previously in the lowerdimensional interactions [1, 2], and d...

In microfluidic applications involving high-frequency acoustic waves over a solid boundary, the Stokes boundary-layer thickness δ is so small that some non-negligible slip may occur at the fluid-solid interface. This paper assesses the impact of this slip by revisiting the classical problem of steady acoustic streaming over a flat boundary, replacing the no-slip boundary condition with the Navi...