Looking for critical nonlinearity in the one-dimensional quasilinear Smoluchowski-Poisson system

Details Looking for critical nonlinearity in the one-dimensional quasilinear Smoluchowski-Poisson system Looking for critical nonlinearity in the one-dimensional quasilinear Smoluchowski-Poisson system

2009-02-19

arxiv.org/abs/0902.3378v1

Mathematics

Analysis of PDEs

Scientific paper

It is known that classical solutions to the one-dimensional quasilinear Smoluchowski-Poisson system with nonlinear diffusion $a(u)=(1+u)^{-p}$ may blow up in finite time if $p>1$ and exist globally if $p<1$. The case $p=1$ thus appears to be critical but it turns out that all solutions are global also in that case. Two classes of diffusion coefficients are actually identified in this paper, one for which all solutions to the corresponding quasilinear Smoluchowski-Poisson system are global and the other one leading to finite time blow-up for sufficiently concentrated initial data. The cornerstone of the proof are an alternative formulation of the Smoluchowski-Poisson system which relies on a novel change of variables and a virial identity.

Affiliated with

Also associated with

No associations

Rating

Looking for critical nonlinearity in the one-dimensional quasilinear Smoluchowski-Poisson system 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 Looking for critical nonlinearity in the one-dimensional quasilinear Smoluchowski-Poisson system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Looking for critical nonlinearity in the one-dimensional quasilinear Smoluchowski-Poisson system will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-260489