Now showing items 1-3 of 3
An annihilating-branching particle model for the heat equation with average temperature zero
We consider two species of particles performing random walks in a domain in [Real numbers] [superscript] d with reflecting boundary conditions, which annihilate on contact. In addition there is a conservation law so that the total number of particles of each type is preserved: When the two particles of different species ...
A Fleming-Viat particle representation of Dirichlet Laplacian
(Springer-Verlag GmbH, 2000-11)
We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. For large N, the particle distribution density converges to the normalized heat equation solution in D ...
The heat equation in time dependent domains with insulated boundaries
(Academic Press (Elsevier), 2004-10)
The paper studies, among other things, two types of possible singularities of the solution to the heat equation at the boundary of a moving domain. Several explicit results on "heat atoms" and "heat singularities" are given.