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自己組織化の方程式～走化性と腫瘍形成
鈴木貴（阪大・基礎工）
ODE
Kinetic
PDE
Stationary
Clustered
Physics
Mathematics
Newton
Jeans-Vlasov
Euler
Semilinear elliptic eigenvalue problem(non-linearity unknown)Hamiltonian flow
Conservation laws
Chaotic motion
Langevin
Kramers-Poisson
Keller-Segel(Smoluchowski)
Semilinear ellipticeigenvalue problem(exponential non-linearity)Gradient flow
Free energy
Quantized blow-up mechanism
0
v
v
ev ave
v
λ
ν
Ω
−∆ + =
∂=
∂
∫ Ω∂Ω
λ
v
8π
1|| ||uλ =
Numerical computation of Childress-Percuss (1981)
Parabolic envelope = infinitely large parabolic region
Hyper-parabola = infinitely small parabolic region
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