| 概要 | This talk is concerned with the existence of global solutions  )
to Cauchy problem of the parabolic-parabolic Keller-Segel system on the plane,
where  and  denote the density of cells and of chemical substance, respectively.
There are a lot of papers of simplified chemotaxis system whose second equation is elliptic.
In such a system,  is a critical mass of that separates the blowup and the global existence.
However the original system has not been quite studied.
I show that if mass of is less than or equal to , then the solution exists globally in time.
Moreover the existence of forward self-similar solutions with mass of greater than is mentioned. |