Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

Details Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

2011-11-07

arxiv.org/abs/1111.1761v1

Mathematics

Analysis of PDEs

Scientific paper

The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, $u_t=J*u-u:=Lu$, in an exterior domain, $\Omega$, which excludes one or several holes, and with zero Dirichlet data on $\mathbb{R}^N\setminus\Omega$. When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is $L$-harmonic, $Lu=0$, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behavior can be presented in a unified way through a suitable global approximation.

Affiliated with

Also associated with

No associations

Rating

Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes 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 Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-52715