On Compact Support Property of Solutions of Hyperbolic Stochastic Partial Differential Equations
by
Oleksiy Ignatyev
Department of Statistics and Probability, Michigan State University
Coauthors: Hassan Allouba

In this paper we investigate the compact support property of the solutions of hyperbolic SPDE providing that initial condition function is deterministic and has compact support property. First, to approach this problem, we consider semi-SPDE. It turns out that in the semi-SPDE case solution u(t, x) preserve compact support property. When we consider SPDE, we use the stochastic differential- difference equations (SDDE) approach. It turns out that in SPDE case solution u(t, x) does not preserve compact support property. So, if we compare the semi-SPDE and SPDE then it becomes obvious that differentiation in space in SPDE plays crucial role and influence the behavior of the solution.

Date received: September 11, 2007