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Convergence of the spectral Galerkin method for the stochastic reaction-diffusion-advection equation
详细信息
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作者:
Li Yang
a
;
li.yang@inria.
fr
"
class
="
auth
_mail" title="E-mail the corresponding
auth
or
;
Yanzhi Zhang
b
;
zhangyanz@mst.edu"
class
="
auth
_mail" title="E-mail the corresponding
auth
or
关键词:
Stochastic reaction&ndash
;
diffusion&ndash
;
advection equation
;
Galerkin approximation
;
Convergence rate
;
Allen&ndash
;
Cahn equation
;
Burgers' equation
刊名:Journal of Mathematical Analysis and Applications
出版年:2017
出版时间:15 February 2017
年:2017
卷:446
期:2
页码:1230-1254
全文大小:1525 K
文摘
We study the convergence of the spectral Galerkin method in solving the stochastic reaction–diffusion–advection equation under different Lipschitz conditions of the reaction function
f
. When
f
is globally (locally) Lipschitz continuous, we prove that the spectral Galerkin approximation strongly (weakly) converges to the mild solution of the stochastic reaction–diffusion–advection equation, and the rate of convergence in
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). The convergence analysis in the local Lipschitz case is challenging, especially in the presence of an advection term. We propose a new approach based on the truncation techniques, which can be easily applied to study other stochastic partial differential equations. Numerical simulations are also provided to study the convergence of Galerkin approximations.
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