応用解析セミナー

過去の記録 ~04/13次回の予定今後の予定 04/14~

開催情報 木曜日 16:00~17:30 数理科学研究科棟(駒場) 002号室
担当者 石毛 和弘

2008年11月13日(木)

16:00-17:30   数理科学研究科棟(駒場) 002号室
杉山 由恵 氏 (津田塾大学・学芸学部・数学科)
Aronson-Benilan type estimate and the optimal Hoelder continuity of weak solutions for the 1D degenerate Keller-Segel systems
[ 講演概要 ]
We consider the Cauchy problem for the 1D Keller-Segel system of degenerate
type (KS)_m with $m>1$:
u_t= \\partial_x^2 u^m - \\partial_x (u^{q-2} \\partial_x v),
-\\partial_x^2 v + v - u=0.
We establish a uniform estimate from below of $\\partial_x^2 u^{m-1}$.
The corresponding estimate to the porous medium equation is well-known
as an Aronson-Benilan type.
As an application of our Aronson-Benilan type estimate,
we prove the optimal Hoelder continuity of the weak solution $u$ of (KS)_m.
In addition, we find that the positive region $D(t):=\\{x \\in \\R; u(x,t)>0\\}$
of $u$ is monotonically non-decreasing with respect to the time $t$.