|
[1]
|
lieb, e. and loss, m. (2001) analysis: vol. 14. 2nd edition, american mathematical society,
providence, ri.
|
|
[2]
|
patlak, c.s. (1953) random walk with persistence and external bias. the bulletin of math-ematical biophysics, 15, 311-338.
|
|
[3]
|
keller, e.f. and segel, l.a. (1970) initiation of slime mold aggregation viewed as an instability.
journal of theoretical biology, 26, 399-415.
|
|
[4]
|
bellomo, n., bellouquid, a., tao, y., et al. (2015) toward a mathematical theory of keller-
segel models of pattern formation in biological tissues. mathematical models and methods
in applied sciences, 25, 1663-1763.
|
|
[5]
|
biler, p. (2020) singularities of solutions to chemotaxis systems. de gruyter, berlin.
|
|
[6]
|
arumugam, g. and tyagi, j. (2021) keller-segel chemotaxis models: a review. acta appli-
candae mathematicae, 171, article no. 6.
|
|
[7]
|
horstmann, d. (2003) from 1970 until present: the keller-segel model in chemotaxis and
its consequences. i. jahresbericht der deutschen mathematiker-vereinigung, 105, 103-165.
|
|
[8]
|
jager, w. and luckhaus, s. (1992) on explosions of solutions to a system of partial differential
equations modelling chemotaxis. transactions of the american mathematical society,
329, 819-824.
|
|
[9]
|
nagai, t. (1995) blow-up of radially symmetric solutions to a chemotaxis system. advances
in mathematical sciences and applications, 5, 581-601.
|
|
[10]
|
dolbeault, j. and perthame, b. (2004) optimal critical mass in the two dimensional keller-
segel model in r2. comptes rendus mathematique, 339, 611-616.
|
|
[11]
|
blanchet, a., dolbeault, j. and perthame, b. (2006) two-dimensional keller-segel model:
optimal critical mass and qualitative properties of the solutions. electronic journal of dif-
ferential equations, 2006, 1-33.
|
|
[12]
|
biler, p., karch, g., laurencot, p., et al. (2006) the 8π-problem for radially symmetric
solutions of a chemotaxis model in the plane. mathematical methods in the applied sciences,
29, 1563-1583.
|
|
[13]
|
blanchet, a., carrillo, j.a. and masmoudi, n. (2008) infinite time aggregation for the critical
patlak-keller-segel model in r2. communications on pure and applied mathematics, 61,
1449-1481.
|
|
[14]
|
kozono, h. and sugiyama, y. (2008) local existence and finite time blow-up of solutions
in the 2-d keller-segel system. journal of evolution equations, 8, 353-378.
|
|
[15]
|
wei, d. (2018) global well-posedness and blow-up for the 2-d patlak-keller-segel equation.
journal of functional analysis, 274, 388-401.
|