Now showing items 1-3 of 3
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.
Stochastic differential equations driven by stable processes for which pathwise uniqueness fails
(North-Holland (Elsevier), 2004-05)
Let Z [subscript] t be a one-dimensional symmetric stable process of order [alpha] with [alpha is an element of the set] (0, 2) and consider the stochastic differential equation dX [subscript] t = [omega] (X [subscript] t−)dZ [subscript]t. For [beta] < 1 [divided by alpha] ^ 1, we show there exists a function that is ...
The Heat Equation and Reflected Brownian Motion in Time-Dependent Domains
(Institute of Mathematical Statistics, 2004-01)
The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as "non-cylindrical domains," and its connections with partial differential equations. Construction is given for reflecting Brownian motion in C3-smooth time-dependent domains in the n-dimensional Euclidean ...