7 papers
Transportation-cost inequalities for invariant measures of stochastic reaction-diffusion equations driven by space-time white noise
Shijie Shang, Tusheng Zhang
In this paper, we establish transportation-cost inequalities for invariant measures of stochastic reaction-diffusion equations driven by multiplicative space-time white noise. In p…
Ergodicity of reflected stochastic reaction-diffusion equations driven by space-time white noise
Shijie Shang, Jianliang Zhai, Tusheng Zhang
We consider the reflected stochastic reaction-diffusion equation on : \begin{align*} \left\{ \begin{aligned} d u(t,x) &=\frac{1}{2}\partial_{xx} u(t,x)dt +b(u(t,x))dt + Ï(u…
Ergodicity of stochastic reaction-diffusion equations on unbounded domains driven by space-time white noise
Shijie Shang, Jianliang Zhai, Tusheng Zhang
We consider the stochastic reaction-diffusion equation on the whole space: \begin{align*} \left\{ \begin{aligned} du(t,x) &=\frac{1}{2}\partial_{xx} u(t,x) dt+b(u(t,x))dt+ Ï(u(t,x…
Stochastic curve shortening flow driven by a transport-type pure jump Lévy noise
Xiaotian Ge, Shijie Shang, Weina Wu +1
We study the existence and uniqueness, the regularity, and the long-time behavior of strong solutions to stochastic curve shortening flow driven by a transport-type pure jump Lévy…
-solutions to stochastic reaction-diffusion equations with superlinear drifts driven by space-time white noise^
Shijie Shang, Pengyu Wang, Tusheng Zhang
Consider the following stochastic reaction-diffusion equation with logarithmic superlinear coefficient b, driven by space-time white noise W: $$ u_t(t,x) = (1/2)u_{xx}(t,x) + b(u(t…
Well-posedness of stochastic partial differential equations with fully local monotone coefficients
Michael Röckner, Shijie Shang, Tusheng Zhang
Consider stochastic partial differential equations (SPDEs) with fully local monotone coefficients in a Gelfand triple : \begin{align*} \left\{ \begin{al…