TY - JOUR
T1 - Effects of the noise level on nonlinear stochastic fractional heat equations
AU - Li, Kexue
N1 - Publisher Copyright:
© 2019 American Institute of Mathematical Sciences. All rights reserved.
PY - 2019/10
Y1 - 2019/10
N2 - We consider the stochastic fractional heat equation ∂tu = 4α/ 2u+ λσ(u)w on [0, L] with Dirichlet boundary conditions, where w denotes the space-time white noise. For any λ > 0, we prove that the pth moment of supx∈[0,L] |u(t, x)| grows at most exponentially. If λ is small, we prove that the pth moment of supx∈[0,L] |u(t, x)| is exponentially stable. At last, we obtain the noise excitation index of pth energy of u(t, x) is (Formula presented.).
AB - We consider the stochastic fractional heat equation ∂tu = 4α/ 2u+ λσ(u)w on [0, L] with Dirichlet boundary conditions, where w denotes the space-time white noise. For any λ > 0, we prove that the pth moment of supx∈[0,L] |u(t, x)| grows at most exponentially. If λ is small, we prove that the pth moment of supx∈[0,L] |u(t, x)| is exponentially stable. At last, we obtain the noise excitation index of pth energy of u(t, x) is (Formula presented.).
KW - Excitation index
KW - Fractional heat kernel
KW - Mittag-Leffler function
KW - Stochastic fractional heat equations
UR - https://www.scopus.com/pages/publications/85072569947
U2 - 10.3934/dcdsb.2019065
DO - 10.3934/dcdsb.2019065
M3 - 文章
AN - SCOPUS:85072569947
SN - 1531-3492
VL - 24
SP - 5437
EP - 5460
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
IS - 10
ER -