TY - JOUR
T1 - Uniqueness and continuity of solution for the initial data in the scaling invariant class of the degenerate Keller-Segel system
AU - Sugiyama, Yoshie
AU - Yahagi, Yumi
PY - 2011/6
Y1 - 2011/6
N2 - We consider the degenerate Keller-Segel system (KS)m below. We find the functional space LS (0, T; Lp(ℝ)N)) with some p,s for the uniqueness and continuity of weak solutions with respect to the initial data. Our space is discussed from a viewpoint of the scaling invariant class associated with (KS)m for γ = 0. The technique is based on the L1-contraction principle for the porous medium equation.
AB - We consider the degenerate Keller-Segel system (KS)m below. We find the functional space LS (0, T; Lp(ℝ)N)) with some p,s for the uniqueness and continuity of weak solutions with respect to the initial data. Our space is discussed from a viewpoint of the scaling invariant class associated with (KS)m for γ = 0. The technique is based on the L1-contraction principle for the porous medium equation.
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U2 - 10.1007/s00028-010-0093-8
DO - 10.1007/s00028-010-0093-8
M3 - Article
AN - SCOPUS:81955160916
SN - 1424-3199
VL - 11
SP - 319
EP - 337
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
IS - 2
ER -