0000000000667019
AUTHOR
Olaf Hansen
On the properties of the radiosity equation near corners
The radiosity equation is an integral equation of the second kind which describes the energy exchange by radiation between surfaces in R3. It is assumed that all surfaces are Lambertian reflectors and that all emitters are diffusive emitters. The radiosity equation plays an important role for the calculation of photo realistic images with the help of computers. Many surfaces which are used in practical calculations are only piecewise smooth and contain edges or corners. In this contribution we present regularity results for the solution of the radiosity equation in the vicinity of corners. The space of piecewise continuous functions is not suitable for this equation and we construct a new f…
ANALYSIS OF A SPHERICAL HARMONICS EXPANSION MODEL OF PLASMA PHYSICS
A spherical harmonics expansion model arising in plasma and semiconductor physics is analyzed. The model describes the distribution of particles in the position-energy space subject to a (given) electric potential and consists of a parabolic degenerate equation. The existence and uniqueness of global-in-time solutions is shown by semigroup theory if the particles are moving in a one-dimensional interval with Dirichlet boundary conditions. The degeneracy allows to show that there is no transport of particles across the boundary corresponding to zero energy. Furthermore, under certain conditions on the potential, it is proved that the solution converges in the long-time limit exponentially f…
The mapping properties of the radiosity operator along an edge
In this article we study the radiosity operator along an edge between two adjacent half-planes. First we show that the radiosity operator is invertible in a whole scale of anisotropic Sobolev spaces. In the absence of any shadows we are able to derive regularity properties of the solution, which depend only on the angle between the half-planes, the reflectivity coefficients and the right-hand side. This work can be considered as a supplement to the article of Rathsfeld (Mathematical Methods in the Applied Sciences 1999; 22: 217–241). Copyright © 2002 John Wiley & Sons, Ltd.