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Heat equation with white or fraction...

Chen, Rui.

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Heat equation with white or fractional noise potentials.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Heat equation with white or fractional noise potentials./
Author:	Chen, Rui.
Description:	63 p.
Notes:	Adviser: Carl Mueller.
Contained By:	Dissertation Abstracts International67-02B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3204548
ISBN:	9780542527388

Heat equation with white or fractional noise potentials.
Chen, Rui.

Heat equation with white or fractional noise potentials. - 63 p.

Adviser: Carl Mueller.

Thesis (Ph.D.)--University of Rochester, 2006.

The asymptotic behavior as t → infinity of the solution of the following stochastic partial differential equation 6ut,x 6t=12 i=1d62 6x2iu t,x+W&d2; x&diam;ut,x u0,x=u0 x0<t<infinity, x∈Rd, is investigated, where W&dot; is a space white noise and the initial condition is u 0(x) a bounded deterministic function. The use of &diam; means that the multiple stochastic integral is considered as the wick product. The solution can be written as the Ito-Wiener chaos expansion. The Lyapunov exponents of the solution in some Lp distribution spaces are estimated. The modulus of continuity of the solution with respect to time or space is explored. Also this paper is concerned with the following stochastic heat equation 6ut,x 6t=12 i=1d62u t,x6x2i +W&d2;H x&diam;ut,x u0,x=u0 x0<t<infinity, x∈Rd where W&dot;H is a time independent fractional white noise with Hurst parameter H = (h1,h2,... hd) and the initial condition is u 0(x) is a bounded deterministic function. The L2 -Lyapunov exponent of the solutions are estimated. We will introduce a family of distribution spaces Sr , rho ∈ R , so that if the solution is in Sr , each chaos of the solution is in L2 . The Lyapunov exponents in Sr of the solutions are also estimated.

ISBN: 9780542527388Subjects--Topical Terms:

515831
Mathematics.

Heat equation with white or fractional noise potentials.
LDR:02121nam 2200265 a 45 001 964191
005 20110901
008 110901s2006 eng d
020 $a 9780542527388
035 $a (UMI)AAI3204548
035 $a AAI3204548
040 $a UMI $c UMI
100 1 $a Chen, Rui. $3 1025253
245 1 0 $a Heat equation with white or fractional noise potentials.
300 $a 63 p.
500 $a Adviser: Carl Mueller.
500 $a Source: Dissertation Abstracts International, Volume: 67-02, Section: B, page: 0923.
502 $a Thesis (Ph.D.)--University of Rochester, 2006.
520 $a The asymptotic behavior as t → infinity of the solution of the following stochastic partial differential equation 6ut,x 6t=12 i=1d62 6x2iu t,x+W&d2; x&diam;ut,x u0,x=u0 x0<t<infinity, x∈Rd, is investigated, where W&dot; is a space white noise and the initial condition is u 0(x) a bounded deterministic function. The use of &diam; means that the multiple stochastic integral is considered as the wick product. The solution can be written as the Ito-Wiener chaos expansion. The Lyapunov exponents of the solution in some Lp distribution spaces are estimated. The modulus of continuity of the solution with respect to time or space is explored. Also this paper is concerned with the following stochastic heat equation 6ut,x 6t=12 i=1d62u t,x6x2i +W&d2;H x&diam;ut,x u0,x=u0 x0<t<infinity, x∈Rd where W&dot;H is a time independent fractional white noise with Hurst parameter H = (h1,h2,... hd) and the initial condition is u 0(x) is a bounded deterministic function. The L2 -Lyapunov exponent of the solutions are estimated. We will introduce a family of distribution spaces Sr , rho ∈ R , so that if the solution is in Sr , each chaos of the solution is in L2 . The Lyapunov exponents in Sr of the solutions are also estimated.
590 $a School code: 0188.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 0 $a University of Rochester. $3 515736
773 0 $t Dissertation Abstracts International $g 67-02B.
790 $a 0188
790 1 0 $a Mueller, Carl, $e advisor
791 $a Ph.D.
792 $a 2006
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3204548