| Abstrakt: |
chaWe study the compact support property for nonnegative solutions of the following stochastic partial differential equations (SPDEs): dtu = aÎJu i (t, x) + cw + h(t, x, u(t, x))F(t, x), (t,x) E (0,oo) x Rd, where F is a spatially homogeneous Gaussian noise that is white in time and colored in space, and h(t,x,u) satisfies K~ 1ux < h(t,x,u) < K(l-\-u) for A 6 (0,1) and K > 1. We show that if the initial data uq > 0 has a compact support, then, under the reinforced Dalang's condition on F (which guarantees the existence and the Hôlder continuity of a weak solution), all nonnegative weak solutions u(t, •) have the compact support for all t > 0 with probability 1. Our results extend the works by Mueller and Perkins [Probab. Theory Related Fields, 93 (1992), pp. 325--358] and Krylov [Probab. Theory Related Fields, 108 (1997), pp. 543--557], in which they show the compact support property only for the one-dimensional SPDEs driven by space-time white noise on (0, oo) x R. [ABSTRACT FROM AUTHOR] |
