TY - JOUR
T1 - Boundedness of solutions to the critical fully parabolic quasilinear one-dimensional Keller–Segel system
AU - Bieganowski, Bartosz
AU - Cieślak, Tomasz
AU - Fujie, Kentarou
AU - Senba, Takasi
N1 - Funding Information:
Bartosz Bieganowski started working on this project during his WCMCS PhD internship at Institute of Mathematics of the Polish Academy of Sciences under supervision of Tomasz Cie?lak, he wishes to thank for the invitation, support and warm hospitality. Kentarou Fujie is supported by Grant-in-Aid for Research Activity start-up (No.?17H07131), Japan Society for the Promotion of Science. Takasi Senba is supported by Grant-in-Aid for Scientific Research (C) (No. 26400172), Japan Society for the Promotion of Science.
Funding Information:
Bartosz Bieganowski started working on this project during his WCMCS PhD internship at Institute of Mathematics of the Polish Academy of Sciences under supervision of Tomasz Cieślak, he wishes to thank for the invitation, support and warm hospitality. Kentarou Fujie is supported by Grant-in-Aid for Research Activity start-up (No. 17H07131), Japan Society for the Promotion of Science. Takasi Senba is supported by Grant-in-Aid for Scientific Research (C) (No. 26400172), Japan Society for the Promotion of Science.
Publisher Copyright:
© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
PY - 2019/4
Y1 - 2019/4
N2 - In this paper we consider a one-dimensional fully parabolic quasilinear Keller–Segel system with critical nonlinear diffusion. We show uniform-in-time boundedness of solutions, which means, that unlike in higher dimensions, there is no critical mass phenomenon in the case of critical diffusion. To this end we utilize estimates from a well-known Lyapunov functional and a recently introduced new Lyapunov-like functional in.
AB - In this paper we consider a one-dimensional fully parabolic quasilinear Keller–Segel system with critical nonlinear diffusion. We show uniform-in-time boundedness of solutions, which means, that unlike in higher dimensions, there is no critical mass phenomenon in the case of critical diffusion. To this end we utilize estimates from a well-known Lyapunov functional and a recently introduced new Lyapunov-like functional in.
KW - Lyapunov-like functional
KW - boundedness of solutions
KW - chemotaxis
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U2 - 10.1002/mana.201800175
DO - 10.1002/mana.201800175
M3 - Article
AN - SCOPUS:85058063444
VL - 292
SP - 724
EP - 732
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
IS - 4
ER -