Preprint:
INTERMITTENCY AND CHAOS FOR A NON-LINEAR STOCHASTIC WAVE EQUATION IN DIMENSION 1

Daniel Conus, Mathew Joseph, Davar Khoshnevisan, and Shang-Yuan Shiu

Abstract. Consider a non-linear stochastic wave equation driven by space-time white noise in dimension one. We discuss the intermittency of the solution, and then use those intermittency result in order to demonstrate that in many cases the solution is chaotic. For the most part, the novel portion of our work is about the two cases where: (1) The initial conditions have compact support, where the global maximum of the solution remains bounded; and (2) The initial conditions are positive constants, where the global maximum is almost surely infinite. Bounds are also provided on the behavior of the global maximum of the solution in Case (2).

Keywords. Intermittency; the stochastic wave equation; chaos

AMS Classification (2000) 60H15; 60H20, 60H05

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)
Shang-Yuan ShiuInstitute of Mathematics, Academia Sinica, Taipei 10617
(shiu [at sign] math [dot sign] sinica [dot sign] edu [dot sign] tw)

Last Update: July 17, 2012
© 2012 - Daniel Conus, Mathew Joseph, Davar Khoshnevisan, and Shang-Yuan Shiu