Decay results for the heat equation under radiation boundary conditions

Near-field infinity-simulating boundary conditions for the heat equation

The numerical simulation of various physical phenomena in infinite domains poses great difficulties. Truncation of the domain is usually necessary in such cases. To ensure stability of the resulting problem on the restricted domain, appropriate boundary conditions should be applied. Here, we develop a boundary condition for the case in which the heat equation is satisfied outside the domain of ...

Positive Solutions for the Beam Equation under Certain Boundary Conditions

We consider a boundary-value problem for the beam equation, in which the boundary conditions mean that the beam is embedded at one end and fastened with a sliding clamp at the other end. Some priori estimates to the positive solutions for the boundary-value problem are obtained. Sufficient conditions for the existence and nonexistence of positive solutions for the boundary-value problem are est...

COMPARISON OF LOCAL RADIATION BOUNDARY CONDITIONS FOR THE SCALAR HELMHOLTZ EQUATION WITH GENERAL BOUNDARY SHAPESy

| The relative accuracy of several local radiation boundary conditions based on the second-order Bayliss{Turkel condition are evaluated. These boundary conditions permit the approximate solution of the scalar Helmholtz equation in an in nite domain using traditional nite element and nite di erence techniques. Unlike the standard BaylissTurkel condition, the generalizations considered here are a...

Absorbing Boundary Conditions for the Schrödinger Equation

A large number of differential equation problems which admit traveling waves are usually defined on very large or infinite domains. To numerically solve these problems on smaller subdomains of the original domain, artificial boundary conditions must be defined for these subdomains. One type of artificial boundary condition which can minimize the size of such subdomains is the absorbing boundary...

New Results on Absorbing Layers and Radiation Boundary Conditions 3