On the Stochastic Heat Equations

Shang-Yuan Shiu

Department of Mathmatics

National Central University

shiu@math.ncu.edu.tw

    We consider the following stochastic heat equation:

`\partial_t u_t(x)=\partial_{xx}u_t(x)+\sigma(u_t(x))\dot{W}(t,x)`,

`x\in(-\infty,\infty)` or `x\in[-1,1]` with certain boundary conditions subject to initial data `u_0(x)`. We will discuss how initial data and the noise term effect the behaviors of the solution. This is based on several different papers.

Keyword: Stochastic heat equations, intermittency, dissipation