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