COLLOQU IUM MATHEMAT I CUM VOL NO
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pages
English
Documents
Obtenez un accès à la bibliothèque pour le consulter en ligne En savoir plus
- self gravitating
- i1 ?
- unique solution
- global existence versus blow up
- paraboli systems
- valued
- similar de ay proles
COLLOQUIUM MATHEMATICUM
m X
∂ u =Δu +∇· c u (∇E ∗u ) , j = 1,...,m,t j j j,h,k h d k
(1)
h,k=1
u(0)(x) =u (x).0
u = (u ,...,u )1 m
d ∞ dR m≥ 1 d≥ 2 c ∈ L (R ) j,h,k = 1,...,mj,h,k
Ed
dR
m = 1 d≥ 2
∂ u =Δu+∇·(u∇ϕ), Δϕ =u.t
u = u(x,t) ϕ
u
cj,h,k
1 u≥ 0
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∂ u =Δu−∇·(u∇ϕ).t
∂ v =Δv−∇·(v∇φ),t
∂ w =Δw +∇·(w∇φ),t
Δφ =v−w.
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−2∼|x|
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|u(x,t)|≤ |u(x,t)|≤ .
2(1+|x|) 1+t
dc (x) Rj,h,k
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lik295
2esssup|x| |u (x)|≤η.0
dx∈R
t → ∞ x → ∞
d/2 d
−2ue(x,t) = 2(d−2)|x|
d≥ 3
du ∈S (R )0 0
∗u t > 0
s,q∗ d˙u(t ) ∈B (R ) s∈R 1≤p,q≤∞p
k·k s,q˙ dB (R )p
pku(t)kL
1≤p≤∞
ub
u
u
C
dR
∇Ed
C
|∇E (x)|≤ .d d−1|x|
∇E K Kd
dR
−d−1+α|K(x)|≤C|x| , 1<α<d.
tgomery-Smith
Chandrasekhar
estimates
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