Preprint:
CORRELATION-LENGTH BOUNDS, AND ESTIMATES FOR INTERMITTENT ISLANDS IN PARABOLIC SPDEs

Daniel Conus, Mathew Joseph, and Davar Khoshnevisan

Abstract. We consider the nonlinear stochastic heat equation in one dimension. Under some conditions on the nonlinearity, we show that the "peaks" of the solution are rare, almost fractal like. We also provide an upper bound on the length of the "islands," the regions of large values. These results are obtained by analyzing the correlation length of the solution.

Keywords. The stochastic heat equation, intermittency, islands, peaks

AMS Classification (2000) Primary: 60H15; Secondary: 35R60.

Support. Research supported in part by the NSF grants DMS-0747758 (M.J.) and DMS-1006903 (D.K.).

Pre/E-Prints. This paper is available in

Daniel ConusLehigh University, Department of Mathematics, Christmas--Saucon Hall, 14 East Packer Avenue, Bethlehem, PA 18015
(daniel [dot sign] conus [at sign] lehigh [dot sign] edu>)
Mathew Joseph &
Davar Khoshnevisan		Department of Mathematics University of Utah, 155 S, 1400 E JWB 233, Salt Lake City, UT 84112-0090, U.S.A.
(joseph [at sign] math [dot sign] utah [dot sign] edu & davar[at sign] math [dot sign] utah [dot sign] edu)

Last Update: October 13, 2011
© 2011 - Daniel Conus, Mathew Joseph, and Davar Khoshnevisan