An asymptotic theory for randomly-forced discrete nonlinear heat equations

Details An asymptotic theory for randomly-forced discrete nonlinear heat equations An asymptotic theory for randomly-forced discrete nonlinear heat equations

2008-11-05

arxiv.org/abs/0811.0643v1

Mathematics

Probability

Scientific paper

We study discrete nonlinear parabolic stochastic heat equations of the form, $u_{n+1}(x) - u_n(x) = (\sL u_n)(x) + \sigma(u_n(x))\xi_n(x)$, for $n\in \Z_+$ and $x\in \Z^d$, where $\bm\xi:=\{\xi_n(x)\}_{n\ge 0,x\in\Z^d}$ denotes random forcing and $\sL$ the generator of a random walk on $\Z^d$. Under mild conditions, we prove that the preceding stochastic PDE has a unique solution that grows at most exponentially in time. And that, under natural conditions, it is "weakly intermittent." Along the way, we establish a comparison principle as well as a finite-support property.

Affiliated with

Also associated with

No associations

Rating

An asymptotic theory for randomly-forced discrete nonlinear heat equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An asymptotic theory for randomly-forced discrete nonlinear heat equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An asymptotic theory for randomly-forced discrete nonlinear heat equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-372929