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Wave equation with white noise and f...

Fang, Bin.

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Wave equation with white noise and fractional white noise potentials.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Wave equation with white noise and fractional white noise potentials./
作者:	Fang, Bin.
面頁冊數:	61 p.
附註:	Source: Dissertation Abstracts International, Volume: 67-02, Section: B, page: 0925.
Contained By:	Dissertation Abstracts International67-02B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3204552
ISBN:	9780542527425

Wave equation with white noise and fractional white noise potentials.
Fang, Bin.

Wave equation with white noise and fractional white noise potentials. - 61 p.

Source: Dissertation Abstracts International, Volume: 67-02, Section: B, page: 0925.

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

The asympototic behavior as t → infinity of the solution of the following stochastic wave equation (SWE) 62utx 6t2=12 n=1d6 2utx 6x2i+w&diam;u tx,0<t<infinity ,x∈Rd is investigated in this paper, where w is a space white noise or a space fractional white noise and the initial conditions are u0(x) = g( x), 6u0x 6t = h(x). The use of &diam; means the Wick product is considered. In chapter 2.1, we show the solution exists in L2 space when d = 1, 2. Accordingly the L2 upper bound and lower bound on the Lyapunov exponents are obtained by using Mittag-Leffier function. In chapter 2.2, we study the SWE with fractional white noise. A L 2 upper bound of the Lyapunov exponent of solution is obtained when 3 + alpha - 2d ∈ (1, 3) and d ≤ 3. In chapter 3.1 and 3.2, the modulus of continuity with both noises are investigated by estimating the second moments of nth chaos differences. In the last chapter 3.3, we study the higher moments (p > 2) of the solution with white noise potentials. For d = 1, 2, the modulus in t does exist. However we can only get the modulus in x for d = 1 case.

ISBN: 9780542527425Subjects--Topical Terms:

515831
Mathematics.

Wave equation with white noise and fractional white noise potentials.
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245 1 0 $a Wave equation with white noise and fractional white noise potentials.
300 $a 61 p.
500 $a Source: Dissertation Abstracts International, Volume: 67-02, Section: B, page: 0925.
500 $a Adviser: Carl Mueller.
502 $a Thesis (Ph.D.)--University of Rochester, 2006.
520 $a The asympototic behavior as t → infinity of the solution of the following stochastic wave equation (SWE) 62utx 6t2=12 n=1d6 2utx 6x2i+w&diam;u tx,0<t<infinity ,x∈Rd is investigated in this paper, where w is a space white noise or a space fractional white noise and the initial conditions are u0(x) = g( x), 6u0x 6t = h(x). The use of &diam; means the Wick product is considered. In chapter 2.1, we show the solution exists in L2 space when d = 1, 2. Accordingly the L2 upper bound and lower bound on the Lyapunov exponents are obtained by using Mittag-Leffier function. In chapter 2.2, we study the SWE with fractional white noise. A L 2 upper bound of the Lyapunov exponent of solution is obtained when 3 + alpha - 2d ∈ (1, 3) and d ≤ 3. In chapter 3.1 and 3.2, the modulus of continuity with both noises are investigated by estimating the second moments of nth chaos differences. In the last chapter 3.3, we study the higher moments (p > 2) of the solution with white noise potentials. For d = 1, 2, the modulus in t does exist. However we can only get the modulus in x for d = 1 case.
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