TY - JOUR
T1 - Global well-posedness of logarithmic Keller-Segel type systems
AU - Ahn, Jaewook
AU - Kang, Kyungkeun
AU - Lee, Jihoon
N1 - Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/6/25
Y1 - 2021/6/25
N2 - We consider a class of logarithmic Keller-Segel type systems modeling the spatio-temporal behavior of either chemotactic cells or criminal activities in spatial dimensions two and higher. Under certain assumptions on parameter values and given functions, the existence of classical solutions is established globally in time, provided that initial data are sufficiently regular. In particular, we enlarge the range of chemotactic sensitivity χ, compared to known results, in case that spatial dimensions are between two and eight. In addition, we provide new type of small initial data to obtain global classical solution, which is also applicable to the urban crime model. We discuss long-time asymptotic behaviors of solutions as well.
AB - We consider a class of logarithmic Keller-Segel type systems modeling the spatio-temporal behavior of either chemotactic cells or criminal activities in spatial dimensions two and higher. Under certain assumptions on parameter values and given functions, the existence of classical solutions is established globally in time, provided that initial data are sufficiently regular. In particular, we enlarge the range of chemotactic sensitivity χ, compared to known results, in case that spatial dimensions are between two and eight. In addition, we provide new type of small initial data to obtain global classical solution, which is also applicable to the urban crime model. We discuss long-time asymptotic behaviors of solutions as well.
KW - Global well-posedness
KW - Logarithmic Keller-Segel
KW - Urban crime
UR - http://www.scopus.com/inward/record.url?scp=85103600175&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2021.03.053
DO - 10.1016/j.jde.2021.03.053
M3 - Article
AN - SCOPUS:85103600175
SN - 0022-0396
VL - 287
SP - 185
EP - 211
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -