Causal diffusion and its backwards diffusion problem

Details Causal diffusion and its backwards diffusion problem Causal diffusion and its backwards diffusion problem

2011-07-20

arxiv.org/abs/1107.3952v2

Mathematics

Analysis of PDEs

In the replacement I have rewritten the abstract and the introduction. Moreover, I have added Remark 1 and simplified a little

Scientific paper

This article starts over the backwards diffusion problem by replacing the \emph{noncausal} diffusion equation, the direct problem, by the \emph{causal} diffusion model developed in \cite{Kow11} for the case of constant diffusion speed. For this purpose we derive an analytic representation of the Green function of causal diffusion in the wave vector-time space for arbitrary (wave vector) dimension $N$. We prove that the respective backwards diffusion problem is ill-posed, but not exponentially ill-posed, if the data acquisition time is larger than a characteristic time period $\tau$ ($2\,\tau$) for space dimension $N\geq 3$ (N=2). In contrast to the noncausal case, the inverse problem is well-posed for N=1. Moreover, we perform a theoretical and numerical comparison between causal and noncausal diffusion in the \emph{space-time domain} and the \emph{wave vector-time domain}. The paper is concluded with numerical simulations of the backwards diffusion problem via the Landweber method.

Affiliated with

Also associated with

No associations

Rating

Causal diffusion and its backwards diffusion problem 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 Causal diffusion and its backwards diffusion problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Causal diffusion and its backwards diffusion problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-35482