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| 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
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 partial2xum−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):=xinR;u(x,t)>0
of u is monotonically non-decreasing with respect to the time t.
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 partial2xum−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):=xinR;u(x,t)>0
of u is monotonically non-decreasing with respect to the time t.
